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Tests for Uniformity: A Comparative Study
Mezbahur Rahman,Shuvro Chakrobartty 한국데이터정보과학회 2004 한국데이터정보과학회지 Vol.15 No.1
The subject of assessing whether a data set is from a specific distribution has received a good deal of attention. This topic is critically important for uniform distributions. Several parametric tests are compared. These tests also can be used in testing randomness of a sample. Anderson-Darling A<sup>2</sup> statistic is found to be most powerful.
Tests for Uniformity : A Comparative Study
Rahman, Mezbahur,Chakrobartty, Shuvro Korean Data and Information Science Society 2004 한국데이터정보과학회지 Vol.15 No.1
The subject of assessing whether a data set is from a specific distribution has received a good deal of attention. This topic is critically important for uniform distributions. Several parametric tests are compared. These tests also can be used in testing randomness of a sample. Anderson-Darling $A^2$ statistic is found to be most powerful.
Likelihood ratio in estimating gamma distribution parameters
Rahman, Mezbahur,Muraduzzaman, S. M. The Korean Data and Information Science Society 2010 한국데이터정보과학회지 Vol.21 No.2
The Gamma Distribution is widely used in Engineering and Industrial applications. Estimation of parameters is revisited in the two-parameter Gamma distribution. The parameters are estimated by minimizing the likelihood ratios. A comparative study between the method of moments, the maximum likelihood method, the method of product spacings, and minimization of three different likelihood ratios is performed using simulation. For the scale parameter, the maximum likelihood estimate performs better and for the shape parameter, the product spacings estimate performs better. Among the three likelihood ratio statistics considered, the Anderson-Darling statistic has inferior performance compared to the Cramer-von-Misses statistic and the Kolmogorov-Smirnov statistic.
A Note on Estimating Parameters in The Two-Parameter Weibull Distribution
Rahman, Mezbahur,Pearson, Larry M. Korean Data and Information Science Society 2003 한국데이터정보과학회지 Vol.14 No.4
The Weibull variate is commonly used as a lifetime distribution in reliability applications. Estimation of parameters is revisited in the two-parameter Weibull distribution. The method of product spacings, the method of quantile estimates and the method of least squares are applied to this distribution. A comparative study between a simple minded estimate, the maximum likelihood estimate, the product spacings estimate, the quantile estimate, the least squares estimate, and the adjusted least squares estimate is presented.
Quantiles for Shapiro-Francia W' Statistic
Rahman, Mezbahur,Ali, Mir Masoom The Korean Data and Information Science Society 1999 한국데이터정보과학회지 Vol.10 No.1
Table of the empirical quantiles for the well known Shapiro-Francia W' goodness of fit statistic is produced which is more accurate than the existing ones. Prediction equation for the quantiles of W' statistic for sample sizes 30 or more we developed. The process of computing the expected values for the standard normal variate is discussed. This work is intended to make the Shapiro-Francia W' statistic more accessible to the practitioner.
Quantiles for Shapiro - Francia W' Statistic
Mezbahur Rahman,Mir Masoom Ali 한국데이터정보과학회 1999 한국데이터정보과학회지 Vol.10 No.1
Table of the empirical quantiles for the well known Shapiro-Francia W` goodness of fit statistic is produced which is more accurate than the existing ones. Prediction equation for the quantiles of W` statistic for sample sizes 30 or more are developed. The process of computing the expected values for the standard normal variate is discussed. This work is intended to make the Shapiro-Francia W` statistic more accessible to the practitioner.
SAMPLE ENTROPY IN ESTIMATING THE BOX-COX TRANSFORMATION
Rahman, Mezbahur,Pearson, Larry M. The Korean Data and Information Science Society 2001 한국데이터정보과학회지 Vol.12 No.1
The Box-Cox transformation is a well known family of power transformation that brings a set of data into agreement with the normality assumption of the residuals and hence the response variable of a postulated model in regression analysis. This paper proposes a new method for estimating the Box-Cox transformation using maximization of the Sample Entropy statistic which forces the data to get closer to normal as much as possible. A comparative study of the proposed procedure with the maximum likelihood procedure, the procedure via artificial regression estimation, and the recently introduced maximization of the Shapiro-Francia W' statistic procedure is given. In addition, we generate a table for the optimal spacings parameter in computing the Sample Entropy statistic.
A note on Box-Cox transformation and application in microarray data
Rahman, Mezbahur,Lee, Nam-Yong The Korean Data and Information Science Society 2011 한국데이터정보과학회지 Vol.22 No.5
The Box-Cox transformation is a well known family of power transformations that brings a set of data into agreement with the normality assumption of the residuals and hence the response variable of a postulated model in regression analysis. Normalization (studentization) of the regressors is a common practice in analyzing microarray data. Here, we implement Box-Cox transformation in normalizing regressors in microarray data. Pridictabilty of the model can be improved using data transformation compared to studentization.
Likelihood ratio in estimating Chi-square parameter
Rahman, Mezbahur The Korean Data and Information Science Society 2009 한국데이터정보과학회지 Vol.20 No.3
The most frequent use of the chi-square distribution is in the area of goodness-of-t of a distribution. The likelihood ratio test is a commonly used test statistic as the maximum likelihood estimate in statistical inferences. The recently revised versions of the likelihood ratio test statistics are used in estimating the parameter in the chi-square distribution. The estimates are compared with the commonly used method of moments and the maximum likelihood estimate.
Shapriro-Francia W' Statistic Using Exclusive Monte Carlo Simulation
Rahman, Mezbahur,Pearson, Larry M. The Korean Data and Information Science Society 2000 한국데이터정보과학회지 Vol.11 No.2
An exclusive simulation study is conducted in computing means for order statistics in standard normal variate. Monte Carlo moments are used in Shapiro-Francia W' statistic computation. Finally, quantiles for Shapiro-Francia W' are generated. The study shows that in computing means for order statistics in standard normal variate, complicated distributions and intensive numerical integrations can be avoided by using Monte Carlo simulation. Lack of accuracy is minimal and computation simplicity is noteworthy.