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INFERENCE FOR RELIABILITY OF A BURR DISTRIBUTION
Ali, M. Masoom,Woo, Jung-Soo,Nadarajah, Saralees The Korean Statistical Society 2007 Journal of the Korean Statistical Society Vol.36 No.4
The distributional properties of Pr(Y<X) and X/(X+Y) and related estimation procedures are derived when X and Y are independent and identically distributed according to the Burr distribution. An application of the results is provided to drought data from Nebraska.
ON THE RATIO X/(X + Y) FOR WEIBULL AND LEVY DISTRIBUTIONS
ALI M. MASOOM,NADARAJAH SARALEES,WOO JUNGSOO The Korean Statistical Society 2005 Journal of the Korean Statistical Society Vol.34 No.1
The distributional properties of R = X/(X + Y) and related estimation procedures are derived when X and Y are independent and identically distributed according to the Weibull or Levy distribution. The work is of interest in biological and physical sciences, econometrics, engineering and ranking and selection.
Some Exponentiated Distributions
Ali, M. Masoom,Pal, Manisha,Woo, Jung-Soo The Korean Statistical Society 2007 Communications for statistical applications and me Vol.14 No.1
In this paper we study a number of new exponentiated distributions. The survival function, failure rate and moments of the distributions have been derived using certain special functions. The behavior of the failure rate has also been studied.
Nonparametric Bayesian Multiple Comparisons for Geometric Populations
Ali, M. Masoom,Cho, J.S.,Begum, Munni The Korean Data and Information Science Society 2005 한국데이터정보과학회지 Vol.16 No.4
A nonparametric Bayesian method for calculating posterior probabilities of the multiple comparison problem on the parameters of several Geometric populations is presented. Bayesian multiple comparisons under two different prior/ likelihood combinations was studied by Gopalan and Berry(1998) using Dirichlet process priors. In this paper, we followed the same approach to calculate posterior probabilities for various hypotheses in a statistical experiment with a partition on the parameter space induced by equality and inequality relationships on the parameters of several geometric populations. This also leads to a simple method for obtaining pairwise comparisons of probability of successes. Gibbs sampling technique was used to evaluate the posterior probabilities of all possible hypotheses that are analytically intractable. A numerical example is given to illustrate the procedure.
Inference for Reliability of a Burr Distribution
M. Masoom Ali,Jungsoo Woo,Saralees Nadarajah 한국통계학회 2007 Journal of the Korean Statistical Society Vol.36 No.4
The distributional properties of Pr(Y < X ) and X=(X + Y) and relatedestimation procedures are derived whenX and Y are independent and iden-tically distributed according to the Burr distribution. An application of theresults is provided to drought data from Nebraska.
Generalized gamma variables with drought application
M. Masoom Ali,우정수,Saralees Nadarajah 한국통계학회 2008 Journal of the Korean Statistical Society Vol.37 No.1
Gamma distributions are some of the most popular models for hydrological processes. Motivated by drought applications, wederive the exact distributions of the productX1X2 and the quotientX1/X2 when X1 and X2 are independent generalized gammarandom variables. An application of the results is provided to drought data from Nebraska.
A Smooth Goodness-of-fit Test Using Selected Sample Quantiles
Umbach, Dale,Masoom Ali, M. The Korean Statistical Society 1996 Journal of the Korean Statistical Society Vol.25 No.3
A new test for goodness-of-fit is presented. It is a modification of a test of LaRiccia (1991). These tests are applicable to continuous lo-cation/scale models. The new test statistic is based on a few selected order statistics taken from the sample, while the LaRiccia test is based directly on the full sample. Each test embeds the hypothesized model in a larger linear model and proceeds to test the goodness-of-fit hy-pothesis by testing the coefficients of this linear model appropriately. The general theory is presented. The tests are compared via computer simulation to a related test of Ali and Umbach (1989) for distributions that could be used as lifetime models. An important aspect of all these tests is that only standard $X_2$ tables are used. Selection of the spacings of the order statistics is discussed.
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.