Power generalized Weibull distribution based on order statistics

Abstract

In this article, we establish recurrence relations for the single and product moments of order statistics from the power generalized Weibull (PGW) distribution due to Bagdonovacius and Nikulin (2002). These recurrence relations enable computation of the means, variances and covariances of all order statistics for all sample sizes in a simple and efficient manner. By using these relations, we have obtained the means, variances and covariances of order statistics from samples of sizes up to 5 for various values of the shape and scale parameters and present them in figures.

Robust Assessment on the Developments of Three Extended Exponential Models with Some New Properties and Applications

“…Voinov et al [68] proposed modified goodness-of-fit tests based on the maximum likelihood of PGW parameters and, through Monte Carlo simulation, showed that power of the tests of the PGW model (cited reference of Bagdonavicȋos and Nikulin [2]) is better than two-parameter Weibull, three-parameter Weibull, and generalized Weibull models. Kumar and Dey [69] developed the recurrence relation for the single and product moments of order statistics from the PGW model and stated that this model is actually due to Bagdonavicȋos and Nikulin [2]. Kumar and Jain [70] obtained explicit expressions for the recurrence relation for the single, product, and conditional moments of order statistics from the PGW model and stated that it is due to Bagdonavicȋos and Nikulin [2].…”

“…Kumar and Dey [69] developed the recurrence relation for the single and product moments of order statistics from the PGW model and stated that this model is actually due to Bagdonavicȋos and Nikulin [2]. Kumar and Jain [70] obtained explicit expressions for the recurrence relation for the single, product, and conditional moments of order statistics from the PGW model and stated that it is due to Bagdonavicȋos and Nikulin [2]. Pandey and Kumari [71] used the Bayesian estimation approach for the parameter estimation of GPW while considering Lindley's approximation and Markov chain Monte Carlo under type-II censoring.…”

Inference on Exponentiated Power Lindley Distribution Based on Order Statistics with Application

“…e values of p r and q r are displayed in Tables 1 and 2 for different values of sample sizes n � 7, 10 and different censoring cases c � 0(1)([n/2] − 1) and for some selected values for υ � 1, 2. e coefficient of the BLUEs p r and q r are given by (17) and (18), respectively, with conditions…”

“…In recent times, several papers and books have been published on order statistics and their distributional properties. Among them are David and Nagaraja [7]; Arnold et al [8]; Balakrishnan and Cohen [9]; Balakrishnan and Ahsanullah [10]; Balakrishnan and Sultan [11]; Malik et al [12]; Mahmoud et al [13]; Genc [14]; MirMostafaee [15]; Balakrishnan et al [16]; Kumar and Dey [17]; Sultan et al [18]; Sultan and AL-ubyani [19]; Kumar et al [20]; and so on. Due to the wide applications of order statistics, several authors have carried out extensive studies on these kinds of ordered data.…”

Power Generalized Weibull Distribution Based on Generalised Order Statistics

“…Let X be a non-negative random variable having an absolutely continuous cdf F (x) with F (0) = 0 and 0 < F (x) < 1 for all x > 0. Then The necessary part follows immediately from equation(17). On the other hand if the recurrence relation in equation(45)is satisfied, then on using equations (4), we have −)] −1 −1 −1 ( ( )) ( ) }.…”