Research Accomplishments

3   Research Publications (46 Papers)

A total of  47 (14 in ISI  journals) have been published or accepted for publication. Research interests include robustness of multivariate analysis, estimation of covariance matrix under loss functions, characterization of probability distributions, survey sampling and the mathematics of descriptive statistics.

 

 

3.1 A Chronological List of Research Publications

 

01.     Ali, M.M. and Joarder, A.H. (1991). Distribution of the correlation coefficient for the class of  bivariate elliptical models. Canadian Journal of Statistics, 19,  447--452. (ISI)

 

02.    Joarder, A.H. and Ali, M.M. (1992 a). Distribution of the correlation matrix for a   class of elliptical models, Communications in Statistics – Theory and  Methods, 21, 1953--1964. (ISI)

 

03.   Joarder, A.H. and Ali, M.M. (1992 b). On some generalized Wishart expectations. Communications in Statistics – Theory and Methods, 21, 283--294. (ISI)

 

04.   Joarder, A.H. (1994). Some applications of  Macdonald function in the multivariate t-distribution. Journal of  Statistical Studies, 14, 115--124.

 

05.   Joarder, A.H. (1995 a). The characteristic function of the univariate t-distribution. Dhaka University Journal of Science, 43, 117--125.

 

06.     Joarder, A.H. and Alam, A.U. (1995). The characteristic function of the elliptical  t distribution using a conditional expectation approach. Journal of Information and Optimization Sciences, 16, 307--310.

07.      Joarder, A.H. (1995 b). Estimation of the scale matrix of a multivariate t-

model.  Journal of Statistical Research, 29, 55-- 66.

 

08.    Joarder, A.H. (1995 c). Estimation of the covariance matrix of the

          multivariate normal distribution. Pakistan Journal of Statistics, 11,

          159--165.

 

09.     Joarder, A.H. and Hossain, M.A. (1995). Estimation of the trace of the scale matrix of   scale mixture of multivariate normal distributions. Journal of Information and Optimization  Sciences, 16, 565--572.

 

10.     Joarder, A.H. and Ali, M.M. (1996 a). On the characteristic function of

  the   multivariate t-distribution. Pakistan Journal of Statistics, 12, 55—

  62.

 

11.   Joarder, A.H. and Ali, M.M. (1996 b). On the characterization of spherical distributions. Journal of Information and Optimization Sciences, 17, 177-- 184.

 

12.   Joarder, A.H. and Ahmed, S.E. (1996). Estimation of  characteristic roots of scale matrix. Metrika, 44, 259--267. (ISI)

 

13.   Joarder, A.H. and Hossain, M.A. (1996). Estimation of the eigenvalues of the scale matrix of a class of elliptical distributions. Statistica, 56, 314--319.

 

14.   Singh, S; Joarder, A.H. and King, M.L. (1996). Regression analysis using   scrambled  responses. Australian Journal of Statistics, 38, 201--211. (ISI)

 

15.   Singh, S. and Joarder, A.H. (1997 a). Unknown repeated trials in randomized response sampling. Indian Society of Agricultural Statistics, 50, 103-105.

 

16.     Singh, S. and Joarder, A.H. (1997 b). Optional randomized response

technique for  sensitive quantitative variable. Metron, 55, 151--157.

 

17.     Joarder, A.H. and Ali, M.M. (1997). Estimation of the scale matrix of a  

multivariate t-model under entropy loss. Metrika, 46, 21--32.  (ISI)

 

18.     Joarder, A.H. and Singh, S. (1997). Estimation of the trace of the scale matrix of a multivariate t-model using regression estimator. Statistics, 28, 161--168.

 

19.     Joarder, A.H. (1997). On the characteristic function of the multivariate Pearson Type II  distribution. Journal of Information and Optimization Sciences, 18, 177—182.

 

20.     Joarder, A.H. and Mahmood, M. (1997). An inductive derivation of Stirling

numbers of  the  second kind and their applications in statistics. Journal of Applied Mathematics and Decision Sciences, 1, 151--157.

 

21.     Joarder, A.H. (1998 a). On the statistical independence in a contingency

table. International Journal of Mathematical Education in Science and Technology 29, 780--782

 

22.     Joarder, A.H. (1998 b).  Some useful Wishart expectations based on the

multivariate  t-model. Statistical Papers, 39, 223--229. (ISI)

 

23.     Singh, S. and Joarder, A.H. (1998). Estimation of finite population

variance using  random non-response  in survey sampling. Metrika, 47, 241--249. (ISI)

 

24.        Joarder, A.H. and Ahmed, S.E. (1998). Estimation of the scale matrix of a

class of  elliptical distributions. Metrika, 48, 149—160. (ISI)

 

25.     Joarder, A.H. and Beg, G.K. (1999). Estimation of the trace of the scale matrix of the multivariate t-model under a squared error loss. Statistica, 59, 181--191.

 

 

Papers Published after having been Promoted to Assoc Prof

 

 26.    Singh, S.,  Joarder, A.H. and Tracy, D.S. (2000). Regression type  

          estimators in the presence of non-response. Statistica, 60, 39-- 44.

 

 27.    Singh, S.,  Joarder, A.H. and Tracy, D.S. (2001). Median estimation using double   sampling. Australian and New Zealand Journal of Statistics, 43, 33-46. (ISI)

 

 28.    Joarder, A.H. and Firozzaman, M. (2001). Quartiles for discrete data.

          Teaching Statistics, 23(3), 86-89.

 

 29.    Ahmed, S.E. ; Volodin, A.I. and Joarder, A.H. (2001). Pretest estimation of eigenvalues of a Wishart matrix. Inernational Mathematical Journal, 1 (3), 259--272.

 

 30.    Firozzaman, M. and Joarder, A.H. (2001). A refinement over the usual

     formulae for deciles. International Journal of Mathematical Education in Science and Technology, 32 (5), 761-765.

 

31.              Joarder, A.H. and Singh, S. (2001). Estimation of the trace of the scaled

covariance matrix of a multivariate t-model using a known information. Metrika, 54 (1), 53-58. (ISI)

 

32.     Joarder, A.H. (2002). Six ways to look at linear interpolation,

     International Journal of Mathematical Education in Science and

     Technology, 32 (6), 932-937.

 

33.   Joarder, A.H. and Al-Sabah, W.S. (2002). The dependence structure of

conditional probabilities in a contingency table. International Journal of Mathematics Education for Science and Technology, 33(3), 475-480.

 

34.              Joarder, A.H. (2002). On some representations of sample variance. International Journal of Mathematics Education for Science and Technology, 33(5), 772-784.

 

35.              Singh, S.  and Joarder, A.H. (2002).Estimation of  the distribution function

and median in two phase sampling. Pakistan Journal of Statistics (S. E Ahmed special issue edited by Serge B. Provost, The University of Western Ontario, Canada), 18(2), 301-319.

 

36.               Joarder, A.H. (2003). The halving method for sample quartiles

          International Journal of Mathematicals Education in Science and

          Technology. 34(4), 629-633. 

 

37.               Joarder, A.H.(2003). The sample variance and first-order Differences of observations. Mathematical Scientist, 28, 129-133.

 

38.               Joarder, A.H. and Latif, R.M. (2004). A  comparison and contrast of

     some methods for sample quartiles. Journal of Probability and Statistical Science,  2(1), 95-109.

 

39.              Barone, L; Voulgaridis, G.Z and Joarder, A.H. (2004). On the dispersion

of data in nonsymmetric distributions. International Journal of Mathematicals Education in Science and Technology35(3), 419-424. 

 

40.    Singh, S., Grewal, I.S. and Joarder, A.H. (2004). General class of

estimators in multicharacter surveys. Statistical Papers, 28, 129-133. (ISI)

 

41.              Joarder, A.H. and Laradji, A. (2005). Algebraic inequalities for measures of dispersion. Journal of Probability and Statistical Science, 3(2), 317-326.

 

42.              Joarder, A.H. and Latif, R.M. (2006). Standard deviation for Small Samples, Teaching Statistics, 28(2), 40-43.

 

43.   Joarder, A.H. (2006a). Product moments of a bivarite Wishart distribution.

        Journal of Probability and Statistical Science, 4(2), 2006, 233-244.

 

44. Kibria, B. M. G. and Joarder A. H. (2006). A short review of multivariate

      t-distribution. Journal of Statistical Research. 40(1), 59-72.

 

45.   Joarder, A.H.  (2006b). Some useful integrals and their applications in 

        correlation  analysis. To  appear in Statistical Papers. (ISI)

 

46.     Laradji, A. and Joarder, A.H. (2006). Inequalities among some measures

of  location. Communications in Statistics – Theory and Methods. 35,

(11). (ISI)

 

47.    Singh, H.P.; Chandra, P; Joarder A.H. and Singh, S. (2006). Family of

estimators of mean, ratio and product of a finite population using random nonresponse. To appear in Test: A Journal of the Spanish Statistical Society. (ISI)

 

 

Papers Submitted or under Revision

 

Joarder, A.H. (2006). Distribution theory with two correlated chisquare variables. Communications in Statistics – Theory and Methods.

 

Joarder, A.H. (2006). A bivariate chisqaure distribution and some of its properties. Submitted to Metrika.

 

Joarder, A.H. (2006). Moments of product and ratio of two correlated chisquare variables. Submitted to Metron.

 

Joarder, A.H.  (2006). A bivariate intregral based on Wishart distribution. Submitted to Journal of Mathematics and Mathematical Sciences.

 

Joarder, A.H. (2006). Skewness and kurtosis for bivariate distributions. Submitted to Statistical Papers.

 

Abujiya, M.R. and Joarder, A.H. (2006). Mahalanobis moments for bivariate chisquare distribution. Submitted to Statistical Papers.

 

Joarder, A.H.  (2006). The expectation of sample variance. Submitted to  Statistica.

 

Joarder, A.H.  and Al-Sabah, W.S. (2006). Probability issues in without replacement sampling. Submitted to A refinement over the usual formulae for deciles.

 

Joarder, A.H. (2006). On a chisquare distribution with a nuisance parameter. Submitted to Statistical Papers.

 

Joarder, A.H. (2006). An introduction to bivariate t-distribuion. Submitted to International Journal of Modern Mathematics.

 

Joarder, A.H. (2006). Moments of the bivariate t-distribution. Submitted to Statistica.

 

Joarder, A.H. and Al-Sabah, W.S. (2006). On the distribution of the norms of spherical distributions. Submitted to Journal of Probability and Statistical Science.

 

Singh, H.P.; Singh, S. and Joarder, A.H. (2006). Estimation of population median when mode of an auxiliary variable is known. Submitted to JSPI.  

 

 

3.2  Statement of Research

 

The major contribution of my research is the development of many foundational results ranging from the distribution theory to the estimation theory for elliptical distributions with emphasis on the multivariate t-distribution. A recent text " Multivariate t Distributions and Their Applications" by Samuel Kotz and Saralees Nadarajah published by Cambridge University Press, UK contains many of  results with 8 references. My research papers have also been cited in reputed research journals, books published by John Wiley and Sons, CRC Press, etc. My research publications can be categorized into the following:

 

(i) Multivariate Estimation Theory

(ii)   Distribution Theory, Moments and Characterizations

(iii) Survey Sampling

(iv) Descriptive Statistics

 

The classical theory of Multivariate Analysis is based on the assumption that underlying observation vectors arise from independent multivariate normal distributions. The multivariate normal distributions have indeed played a predominant role in the historical development of statistical theory, and found applications in physical, biological, engineering  and other branches of science and business.

 

Samuel Kotz (1975) presented a systematic classification of multivariate distributions based on various criteria such as type of dependence, analogy of mathematical form, model and characterizations. Kelker (1970) was the first statistician to develop statistical theory for multivariate elliptical distributions, a class of distributions which accommodates  multivariate t-distribution and multivariate normal distribution as special cases. Fang and Anderson (1990) edited a book on multivariate elliptical distributions. Fang and Zhang (1990) were the first to come up with a  book on multivariate analysis with elliptical distributions.

 

The multivariate t-distribution has fatter tails and can characterize many financial data especially stock return data.  Zellner (1976) laid the foundation for modeling financial data under the assumption that observations follow t-distribution. Since then many authors tried to develop statistical theory for a t-population.

 

Multivariate Estimation Theory (11 Papers)

 

There have been numerous papers on the estimation of the covariance matrix of the multivariate normal distribution.  Maximum likelihood method has been one of the most popular method of estimation for the covariance matrix. The most powerful property of the maximum likelihood estimator is the asymptotic normality which stems out, in fact,  from the independence of the sample observations. However the assumption of the independence of the observations for multivariate elliptical distributions is true only for the special case of multivariate normal distribution. So some authors have tried to estimate the covariance by the criteria of  loss functions. 

 

In a series of papers estimation strategies for covariance matrix of the multivariate t-distribution, its trace, characteristics roots etc have been developed under squared error loss function [Joarder (1995 b), Joarder and Ahmed (1996), Joarder and Beg (1999)]. The covariance matrix of the multivariate t-distribution has also been estimated under an entropy loss function (Joarder and Ali, 1997). Trace and covariance matrix of the scale mixture of multivariate normal distributions have also been studied [Joarder and Hossain (1995), Joarder and Ahmed (1998)]. The covariance matrix of the multivariate t-distribution has been estimated by the use

 

of a regression type of estimator( Joarder and Singh ,1997) and also by using a known information  (Joarder and Singh, 2001). The covariance matrix based on multivariate normal distribution has been estimated by Joarder (1995c). Eigenvalues of a Wishart matrix based on multivariate normal distribution has been estimated by Pretest Method (see Ahmed, Volodin and Joarder, 2001)

 

Distribution  Theory, Moments and Characterizations  (13  Papers)

 

The distribution of the correlation coefficient based on bivariate elliptical distributions has been derived  (Ali and Joarder, 1991). This proves the robustness of the distribution correlation coefficient in the wider class of bivariate elliptical distributions and t-test for the uncorrelatedness. The distribution theory has been extended to multivariate elliptical distributions to derive the distribution of correlation matrix (Joarder and Ali, 1992).  Some integral results with applications to correlation analysis have been developed (Joarder, 2006b).

 

Characteristic functions of several multivariate distributions say Multivariate t-distribution, Multivariate Pearson Type II Distribution, Uniform Distribution on or inside Unit Hyper-Sphere  etc have been derived in terms of  well known special functions  [Joarder (1995 a), Joarder and Alam (1995), Joarder and Ali (1996 a), Joarder (1997)]. Spherical Distributions, a special class of elliptical distributions, have been characterized geometrically and analytically (Joarder and Ali ,1996 b). Some applications of  Macdonald function in the multivariate t-distribution has been discussed (Joarder, 1994). Stirling numbers of the second kind has been derived by an inductive method and applied to find moments of  integer valued random variables (Joarder and Mahmood ,1997).  

 

Identities involving Wishart matrix based on the multivariate t-distribution have been derived ( Joarder and Ali ,1992 b). Some useful expected values of  important functions of Wishart matrices based on the multivariate t-model has been derived (Joarder, 1998 b). These are important for the loss theoretic estimation of covariance matrix and its characteristics. Product moments of bivariate Wishart distribution have been derived (Joarder, 2006a).

 

Survey Sampling (10  Papers)

 

Scrambled randomized response method has been applied to  linear regression model (Singh, Joarder and King , 1996).  Optional randomized response technique has been developed for sensitive qualitative variable (Singh and Joarder, 1997 b).

 

Finite population variance has been estimated by the use of random non-response (Singh and Joarder 1998). Unknown repeated trials in randomized response sampling has been considered by Singh and Joarder (1997 a). Regression type estimators in the presence of non-response has been discussed by Singh, Joarder and Tracy (2000). Some regression type estimators have been studied for random

non-response in different situations under the assumption that the number of sampling units on which information cannot be obtained due to random non-response follows some probability distribution (see Singh, Joarder and Tracy (2001).

 

Distribution function and median in two phase sampling have been estimated by Singh and Joarder (2002). General class of estimators in multicharacter surveys is

considered in Singh, Grewal and Joarder (2004). Singh, Chandra , Joarder and Singh (2006)  have developed family of estimators of mean, ratio and product of a finite population under random nonresponse.

 

Descriptive Statistics and Miscellaneous (12 Papers)

 

It has been proved that statistical independence and linear dependence of a square contingency matrix are equivalent (Joarder, 1998 a). The dependence structure of conditional probabilities in a square contingency table has been considered by Joarder and Al-Sabah ( 2002). A halving method  (Joarder 2003) has been proposed for the quartiles. A remainder method (Firozzaman  and Joarder, 2001) has been proposed for quartiles and deciles . Linear interpolation has been viewed by Joarder (2002) from six different perspectives. Sample variance has been calculated by Joarder (2002) without the use of sample mean and by Joarder

 

(2003) by the first order differences of observations. A comparison and contrast for sample quartiles has been considered by Joarder and Latif (2004). Some inequalities among some measures of location have been developed by Laradji and Joarder (2006). Algebraic inequalities have been developed by Joarder and Laradji (2005) for measures of dispersion.

 

 

References

 

Kelker, D. (1970). Distribution theory of spherical distributions and a location scale parameter generalization. Sankhya, Ser. A, 32, 419—430.

 

Kotz, S. (1975). Multivariate distributions at a cross-road. In Statistical Distributions in Scientific Work, (eds. G.P. Patil, S. Kotz and J.K. Ord, D. Reidel Publ. Co.), 1,  247—270.

 

Fang, K.T. and Anderson, T.W. (1990). Statistical Inference in Elliptically Contoured and Related Distributions. Allerton Press, New York.

 

Fang, K.T. and Zhang, Y. (1990). Generalized Multivariate Analysis. Springer Verlag.

 

Zellner, A. (1976). Bayesian and non-Bayesian analysis of the regression model with multivariate Student-t error term.  Journal of American Statistical Association, 71, 400—405 (correction, 71, 1000).

 

For other references see Section 3.1 of the CV.

 

 

 

3.3 Books Under Preparation

 

Hassen A. Muttlak; Anwar H. Joarder and Walid S. Al-Sabah (2004). " Laboratory

Manual for Probabilty and Statistics for Engineers and Scientists" , KFUPM

Press, Dhahran,  Saudi Arabia. (137 pages of size 21 x 29 cm,  ISBN 9960-07-

205-03). This has been used in the dept since the beginning of 2004.

 

Drafted  a book entitled “ Statistics for  Science, Engineering and

Technology”. The manuscript is of  350 pages typed up in A-4 size paper and

divided into ten chapters.

 

Drafted a book  entitled  “Teaching Basic Statistics” based on my pedagogical

publications.

 

Kibria, B.M.G and Joarder, A.H. "Multivarite T-Distribution and its Application in Regression Analysis".

 

 

3.4  Research Papers in Citation (31 Citations)

 

 

Paper Title

Citation

1

 

Joarder A.H. and Ali, M.M.  (1992). The distribution of correlation matrix for a class of elliptical models. Communications in Statistics -  Theory & Methods, 21 (7),  1953-1964.

 


Mathai, A.M. (1993).  The residual effect of growth-decay mechanism and the distributions of covariance structures. Canadian Journal of Statistics,  21 (3),  277-283.

2

Ali, M.M. and Joarder, A.H.  (1991). Distribution of the correlation coefficient for the class of bivariate elliptical models. Canadian Journal of Staistics,  19 (4), 447-452. (Dec 1991)

 

Arellano Valle R.B., Bolfarine, H. (1996). Elliptical structural models. Communications in Statistics -  Theory & Methods,  25 (10),  2319-2341.

 3

Joarder, A.H. and Ali, M.M. (1992).On some generalized Wishart expectations. Communications in Statistics – Theory and Methods, 21, 283-294.

Gupta, A.K. and Nagar, D.K. (2000). Matrix Variate Distributions. Chapman and Hall. London.

 

4

Joarder, A.H. (1997). On the Characteristic function of multivariate Pearson Type II distribution. Journal of Information & Optimization Sciences, 18, 177-182.

Johnson, N.L., Balakrishnan, N. and Kotz, S. (2000). Continuous Multivariate Distributions (Volume 1, Models and Applications). Wiley, New York (pp9-10).

 

 

5

Singh, S. and  Joarder, A.H. (1998). Estimation of finite population variance using random non-response in survey sampling , Metrika, 47 (3),  241-249.

Singh, S and Horn, S. (2000). Compromised imputation in survey sampling, Metrika, 51 (3),  267-276 2000

6

Ali, M.M. and  Joarder, A.H. (1991). Distribution of the correlation coefficient for the class of bivariate elliptical models. Canadian Journal of Staistics,  19 (4), 447-452. 

 

Yuan, K.H. and Bentler, P.M. (2000) Inferences on correlation coefficients in some classes of nonnormal distributionsJournal of Multivariate Analysis, 72 (2),  230-248. View full text from the publisher EBSCO

7

Ali,  M.M. and Joarder, A.H.  (1991). Distribution of the correlation coefficient for the class of bivariate elliptical models. Canadian Journal of Staistics,  19 (4), 447-452. 

 

Mudholkar GS, Wilding GE, Mietlowski WL (2003). Robustness properties of the Pitman-Morgan testCommunications in Statistics -  Theory & Methods, 32(9), 1801-1816.  View full text from the publisher EBSCO

8

Singh, S., Joarder, A.H. and Tracy, D.S., (2001) Median estimation using double sampling. Australian and New Zealand Journal of Statistics,  43 (1), 33-46.

Arcos, A.C. ; Gonzalez, S.A.; Martmez, M.D.; Roman, Y.M. and Rueda, M.M. (2003). Estimating quantiles in population subject to change. ISI\E&H International Conference on Environmental Statistics and Health, Saddiago de Compostela.

9

Ali,  M.M. and Joarder, A.H.  (1991).

 

Distribution of the correlation coefficient for the class of bivariate elliptical models. Canadian Journal of Staistics,  19(4), 447-452. (Dec 1991)

 

 Yuan, K.H. and Bentler, P.M. (2004). On the asymptotic distributions of two statistics for two-level covariance structure models within the class of elliptical distributions . Psychometrika, 69(3), 437-457

 

10

Singh, S. and  Joarder, A.H. (1998). Estimation of finite population variance using random non-response in survey sampling , Metrika, 47 (3), 241-249.

 

Rueda, M. and Gonzalez, S. (2004).  Missing data and auxiliary information in surveys. Computational Statistics,  19(4), 551-567.

11

Singh, S.;  Joarder, A.H. and  Tracy,  D.S.  (2001) Median estimation using double sampling. Ausatralian & New Zealand Journal of Statistics, 43 (1), 33-46.

 

Rueda, M. and  Arcos, A. (2004). Improving ratio-type quantile estimates in a finitepopulationStatistical Papers, 45 (2),  231-248

 

 

 12

Joarder, A.H. and Ahmed, S.E.  (1998). Estimation of the scale matrix of a class of elliptical distributions. Metrika,  48 (2), 149-160.

 

Nadarajah, S. and Kotz, S. (2005). Sampling distributions associated with the multivariate t distribution. Statistica Neerlandica, 59 (2),  214-234.

13

Joarder, A.H. and Ali, M.M. (1992). On some generalized Wishart expectations. Communications in Statistics – Theory and Methods, 21, 283--294.

Kotz, S. and  Nadarajah, S. (2004). Multivariate t Distributions and Their Applications. (Cited on pages 193, 256) Cambridge University Press in 2004.

 

14

Joarder, A.H. and Ahmed, S.E. (1996). Estimation of  characteristic roots of scale matrix. Metrika, 44, 259--267.

Kotz, S. and  Nadarajah, S. (2004). Multivariate t Distributions and Their Applications. (Cited on page 191, 255) Cambridge University Press in 2004.

 

15

Joarder, A.H. and Ali, M.M. (1996). On the characteristic function of the   multivariate t-distribution. Pakistan Journal of Statistics, 12, 55—62.

 Kotz, S. and  Nadarajah, S. (2004). Multivariate t Distributions and Their Applications. (Cited on pages 36-39 in a Section 2.2: Joarder and Ali's Approach and also on 256) Cambridge University Press in 2004.

 

16

Joarder, A.H. (1998 ).  Some useful Wishart expectations based on the   multivariate  t-model. Statistical Papers, 39, 223--229.

Kotz, S. and  Nadarajah, S. (2004). Multivariate t Distributions and Their Applications. (Cited with results running 22 lines on pages 193-194 and 255). Cambridge University Press.

 

17

Joarder, A.H. and Ali, M.M. (1997). Estimation of the scale matrix of a   multivariate t-model under entropy loss. Metrika, 46, 21--32.

 

Kotz, S. and  Nadarajah, S. (2004). Multivariate t Distributions and Their Applications. (Cited with results running 22 lines on pages 191-192 and 256). Cambridge University Press.

 

18

Joarder, A.H. and Ahmed, S.E. (1998). Estimation of the scale matrix of a class of elliptical distributions. Metrika, 48, 149—160

Kotz, S. and  Nadarajah, S. (2004). Multivariate t Distributions and Their Applications. (Cited with results running 22 lines on pages 222-223 and 256). Cambridge University Press.

19

Joarder, A.H. (1995). Estimation of the trace of the scale matrix of a multivariate t-model, in Proceddings of the Econometric Conferernce, pp 467-474 (Monash University, Australia)

Kotz, S. and  Nadarajah, S. (2004). Multivariate t Distributions and Their Applications. (Cited on pages 221 and 255). Cambridge University Press.

20

Joarder, A.H. and Singh, S. (1997). Estimation of the trace of the scale matrix of a multivariate t-model using regression estimator. Statistics, 28, 161--168.

 

Kotz, S. and  Nadarajah, S. (2004). Multivariate t Distributions and Their Applications. (Cited with results running 28 lines on pages 221-222 and 256). Cambridge University Press.

 

21

Singh, S., Joarder, A.H. and King, M.L. (1996), Regrassion analysis using scrambled responses. Australian Journal of Statistics, 38(2): 201—211.

Singh, H.P. and Mathur, N.  (2004). Estimation of Population mean with known coefficient of variation under optional randomized response model using scrambled response technique. Statistics in Transition, 6(7), 1079—1093.

22

Joarder, A.H. and M. Firozzaman  (2001). Quartiles for discrete data. Teaching Statistics, 23(3), 86-89"

Highlighted in the homepage (http://www.blackwellpublishing.com/journal.asp?ref=0141-982X)  in 2004.

 

23

Singh, S. and Joarder, AH. (1998). Estimation of finite population variance using randomnon-response in survey sampling. Metrika, 47,  241-249,

 

Ahmed, M.S.; Titi, O.; Al-Rawib, Z. and Abu-Dayyeh, W. (2005). International Journal of Information and Management Sciences, 6, 2, 73-82;

 

24

Singh, S. and Joarder, AH. (1998). Estimation of finite population variance using randomnon-response in survey sampling. Metrika, 47,  241-249,

 

Rueda, M.; Gonzalez, S. and Arcos, A. (2006). Estimating the difference between two means with missing data in sample surveys. Model Assisted Statistics and Applications, 1, 51-56.

25

Singh, S.; Joarder, A.H. and Tracy, D.S. (2001). Median estimation using double sampling, Ausatralian & New Zealand Journal of Statistics, 43 (1),  33-46.

 

 Arcos, A.;  Rueda, M. and  Martinez-Miranda,  D (2005).
Using multiparametric auxiliary information at the estimation stage, Statistical Papers,  46 (3), 339-358.

 

26

Joarder,  A.H. and  Ali,  M.M(1997).  Estimation of the scale matrix of a multivariate t-Model under entropy loss,  Metrika, 46 (1),  21-32.

 

Nadarajah, S. and  Kotz,  S. (2005). Sampling distributions associated with the multivariate t distribution. Statistica, Neerlandica, 59 (2),  214-234.  View full text from the publisher EBSCO

 

27

Joarder,  A.H. and  Ali,  M.M(1997).  Estimation of the scale matrix of a multivariate t-Model under entropy loss,  Metrika, 46 (1),  21-32.

 

Petropoulos, C. and  Kourouklis,  S. (2005). Estimation of a scale parameter in mixture models with unknown location Journal of Statistical Planning and Inference, 128 (1), 191-218.

28

Joarder,  A.H. and  Ahmed,  S.E.  (1996). Estimation of the characteristic roots of the scale matrix Metrika, 44 (3), 259-267.

 

Nadarajah,  S. and Kotz,  S. (2005). Sampling distributions associated with the multivariate t distribution. Statistica Neerlandica, 59 (2),  214-234.  View full text from the publisher EBSCO

 

29

Joarder, A.H. and  Ahmed, S.E. (1996). Estimation of the characteristic roots of the scale matrix. Metrika, 44 (3), 259-267.

 

Ahmed, S.E. (1998). Large-sample estimation strategies for eigenvalues of a Wishart matrix . Metrika, 47 (1), 35-45 1998  View full text from the publisher EBSCO

30

Joarder, A.H. 1998). Some useful Wishart expectations based on the multivariate t-model. Statistical Papers,  39 (2),  223-229.

Nadarajah, S. and Kotz, S. (2005). Sampling distributions associated with the multivariate t distributionStatistica Neerlandica, 59 (2),  214-234.  View full text from the publisher EBSCO
 

31

Singh, S.; Joarder, A.H. and Tracy, D.S. (2000). Regression type estimators for random nonresponse in survey sampling, Statistica, 60, 39-44.

Rueda, M.; Gonzalez, S. and Arcos, A. (2006). Estimating the difference between two means with missing data in sample surveys. Model Assisted Statistics and Applications, 1, 51-56.

32

Singh, S.; Joarder, A.H. and Tracy, D.S. (2001). Median estimation using double sampling, Ausatralian & New Zealand Journal of Statistics, 43 (1),  33-46.

 

Singh, S.; Singh, H.P. and Upadhaya, L.N. (2006). Chain ratio and regression type estimators for median estimation in survey sampling, Statistical Papers, 48(1), 23-46.

 

33

Joarder, A.H. and Firozzaman, M.

(2001). Quartiles for discrete data.

Teaching Statistics, 23(3), 86-89.

Langford, Eric (2006). Quartiles in Elementary Statistics, Journal of Statistics Education, 14(3),www.amstat.org/publications/jse/v14n3/langford.html

 

 

3.5  Papers or Abstracts in Conferences (8)

 

Joarder, A.H. (2004). Sample variance and first order differences in

observations. Abstract published in the Proceedings of the Seventh Meeting of

SAMS (Saudi Association for Mathematical Sciences) held between April 7-8,

2004 in Prince Sultan University, Riyadh, Saudi Arabia.

 

Laradji, A. and Joarder, A.H. (2004). Inequalities involving means and quantiles.

Abstract published in the Proceedings of the Seventh Meeting of SAMS (Saudi

Association for Mathematical Sciences) held between April 7-8, 2004 in Prince

Sultan University, Riyadh, Saudi Arabia.

 

Firozzaman, M. and Joarder, A.H. (2001). A Refinement over the usual formulae

for deciles. Published in the Proceedings “Biology, Earth Sciences and

Mathematics” pp 371-376 of the First Saudi Science Conference,  KFUPM,

Saudi Arabia.

 

Joarder, A.H. and Ahmed, S.E. (1999). Estimation of the scaled covariance

matrix of a class of elliptical distributions. Abstracted on pages 88-89 as

Manuscript Number 137 in  the Proceeding of the 27th Annual Meeting of

Statistical Society of Canada held at University of Regina, Regina, Saskatchewan

during June 8-June 9, 1999. 

 

Joarder, A.H. (1999). Robustness of product-moment correlation coefficient

under a  broader class of distributions. Abstracted in the Abstracts of

Presented Papers, page 5. The  Fourth Meeting of the Saudi Association for 

Mathematical Sciences held during  March 9-10, 1999 at King Saud University,

Riyadh, Saudi Arabia.

 

Singh, S. and Joarder, A.H. (1996). Estimation of finite population variance using random non-response in survey sampling. Abstracted in Sydney Meeting

 

Abstracts, pages 100--101.  Sydney International Statistical Congress 1996 held in  Sydney, Australia.

 

Joarder, A.H. (1995). Estimation of the trace of the scale matrix of a multivariate

t-model. Proceeding of the Econometrics Conference at Monash, pages 467—

474,   Monash University, Australia.

 

 

 

 

3.6         Technical Reports (34)

 

Skewness and Kurtosis for Bivariate distributions. Technical Reoprt No. 363 (November 2006), Dept of Mathematical Sciences, KFUPM, Saudi Arabia 

 

Joarder, A.H. and Kibria, B.M.G. (2006). A Modest Introduction to Uncorrelated T-Model. Technical Reoprt No. 354 (May 2006), Dept of Mathematical Science, KFUPM, Saudi Arabia 

 

Joarder, A.H. and Walid S. Al-Sabah (2006). On the distributions of Norms of Spherical Distributions. Technical Report No. 349 (May 2006), Department of  Mathematical Sciences, KFUPM,   Saudi Arabia

 

Joarder, A.H. (2006). An Introduction to the Bivariate T-Distribution. Technical Report No. 345 (Mar 2006), Department of  Mathematical Sciences, KFUPM,   Saudi Arabia

 

Sing, H.P.; Chandra, P.; Joarder, A.H. and Singh, S. (2006). Family of estimators of mean, ratio and product of a finite population using random nonresponse. Technical Report No. 344 (Mar 2006), Department of  Mathematical Sciences, KFUPM,   Saudi Arabia.

 

Joarder, A.H. (2006). Mahalanobis Moments of the Bivariate Chisqaure Distribution Distribution. Technical Report No. 350 (May 2006), Department of  Mathematical Sciences, King Fahd University of Petroleum and Minerals,  Dhahran,   Saudi Arabia

 

Joarder, A.H. (2006). Moments of the Bivariate T-Distribution. Technical Report No. 346 (Mar 2006), Department of  Mathematical Sciences, KFUPM,   Saudi Arabia

 

Joarder, A.H. (2006). Standardized Moments of Bivariate Distributions. Technical Report No. 347 (Mar 2006), Department of  Mathematical Sciences, KFUPM,   Saudi Arabia

 

Joarder, A.H. and Abujiya, M.R. (2006). The Remainder Method for Sample Percentiles. Technical Report No. 343 (Jan 2006), Department of  Mathematical Sciences, KFUPM,   Saudi Arabia

 

Joarder, A.H. (2005). Moments of the Product and Quotient of Two Correlated Chisquare Random Variables. Technical Report No. 341 (Dec 2005), Department of  Mathematical Sciences, KFUPM, Saudi Arabia.

 

Joarder, A.H. (2005). A Bivariate Integral Based on Wishart Distribution. Technical Report No. 339 (Dec 2005), Department of  Mathematical Sciences, KFUPM,  Saudi Arabia.

 

Joarder, A.H. and Al-Sabah, W.S. (2005). Probability Issues in Without Replacement Sampling. Technical Report No. 342 (Dec 2005), Department of  Mathematical Sciences, KFUPM,   Saudi Arabia.

 

Joarder, A.H. (2005). Some Useful Integrals and Their Applications in Correlation Analysis. Technical Report No. 338 (Nov 2005), Department of  Mathematical Sciences, KFUPM,   Saudi Arabia.

 

Joarder, A.H. (2005). On a Bivariate Chisquare Distribution. Technical Report No. 335 (June), Department of  Mathematical Sciences, KFUPM,   Saudi Arabia.

 

Joarder, A.H. (2005). Product Moments of Bivariate Wishart Distribution. Technical Report No. 330 (May), Department of  Mathematical Sciences, KFUPM,   Saudi Arabia.

 

Joarder, A.H. and Latif, R.M. (2005). Standard Deviation for Small Samples.

Technical Report No. 329 (May), Department of  Mathematical Sciences, KFUPM,  

Saudi Arabia.

 

Joarder, A.H. (2005). The Expected Sample Variance in a General Situation.

Technical Report No. 328 (May), Department of  Mathematical Sciences, King

Fahd University of Petroleum and Minerals,  Dhahran,   Saudi Arabia.

 

Joarder, A.H. (2004). Some inequalities in Descriptive Statistics. Technical Report

No. 321 (June), Department of  Mathematical Sciences, KFUPM,   Saudi Arabia.

 

Joarder, A.H. (2002). Sample variance and the first order differences of observations. Technical Report No. 293, Department of  Mathematical Sciences, KFUPM,  Saudi Arabia.

 

Laradji, A. and Joarder, A.H. (2002). Inequalities involving sample means, median and extreme observations. Technical Report No. 283 (October), Department of  Mathematical Sciences, KFUPM, Saudi Arabia.

 

Joarder, A.H. (2002). The moments of a discrete distribution associated with the

principle of inclusion and exclusion. Technical Report No. 277, Department of 

Mathematical Sciences, KFUPM, Saudi Arabia.

 

Joarder, A.H. (2002). The moments of a discrete distribution associated with the

principle of inclusion and exclusion. Technical Report No. 277, Department of 

Mathematical Sciences, KFUPM, Saudi Arabia.

 

Joarder, A.H. (2002). The Remainder Method for  Sample Quartiles of Even

Order. Technical Report No. 274, Department of  Mathematical Sciences, KFUPM,  

Saudi Arabia.

 

Joarder, A.H. (2002). The Hinge Method and the Halving Method for Sample

quartiles. Technical Report No. 273, Department of  Mathematical Sciences, King

Fahd University of Petroleum and Minerals,  Dhahran,   Saudi Arabia.

 

Singh, S. and Joarder, A.H. (2001). Estimation of Distribution Function and

Median in Two Phase sampling, Technical Report No. 270, Department of    

Mathematical Sciences, King Fahd University of Petroleum and Minerals,       Dhahran, Saudi Arabia.

 

Joarder, A.H. (2001). On some representations of sample variance. Technical

Report  No.  269, Department of Mathematical Sciences, KFUPM, Saudi Arabia.

 

Joarder, A.H. and Al-Sabah, Walid S. (2001) The dependence structure of

conditional probabilities in a contingency table. Technical Report  No. 260,  Department of Mathematical Sciences, KFUPM, Saudi Arabia.

 

Firozzaman, M. and Joarder, A.H. (2000). A refinement over the usual formulae

for quartiles. Technical Report  No. 254,  Department of Mathematical Sciences,

KFUPM, Saudi Arabia.

 

Joarder, A.H. (1999). A class of improved estimators for the elliptical model

under the entropy loss function. Technical Report  No. 249,  Department of

Mathematical Sciences, King Fahd University of Petroleum and Minerals, 

Dhahran, Saudi Arabia.

 

Joarder, A.H. and Beg, G.K. (1999). Estimation of the trace of the scale matrix of

a multivariate t-model under a squared error loss. Technical Report  No. 243, 

Department of Mathematical Sciences, KFUPM, Saudi Arabia.

 

Joarder, A.H. and Ahmed (1998). Estimation of the scale matrix of a class of

elliptical distributions. Technical Report No. 235,  Department of Mathematical

Sciences, KFUPM, Saudi Arabia.

 

Joarder, A.H. and Singh, S. (1998). Estimation of the trace of the scaled

covariance matrix of a multivariate t-model using a power transformation. 

Technical Report No. 234, Department of Mathematical Sciences, KFUPM, 

Saudi Arabia.

 

Joarder, A.H. and Mahmood, M. (1998). On the statistical theory of a t-

population. Technical Report No. 231, Department of Mathematical Sciences,

KFUPM,  Saudi Arabia.

 

Joarder, A.H. and Mahmood, M.  (1997). An inductive derivation of Stirling

numbers of  the  second kind and their applications in statistics. Technical Report

No. 225, Department of Mathematical Sciences, KFUPM, Saudi Arabia.

 

 

 3.7 Research Funds

 

Obtained Faculty Research Grant 1995 of an amount of $3500.00 for the project  “Estimation of the Scale Matrix of a T-model under Quadratic Loss Function” by the Faculty of Business and Economics Research Committee, Monash University, Victoria,  Australia.

 

Obtained Fast Track Research Grant FT 2004-22 on the proposal "Product Moments of Bivariate Wishart Distribution" (Coinvestigator, Mr M.R. Abujiya). The project is very well in progress.

 

Obtained Fast Track Research Grant FT 2004-23 on the proposal "Expectations for Inverted Wishart Distribution" (Coinvestigator, Dr R.M. Latif). The project is very well in progress.