Abstract
In this paper, we developed a new distribution, namely the two parameters Rani distribution (TPRD). Some statistical properties of the proposed distribution are derived including the moments, moment-generating function, reliability function, hazard function, reversed hazard function, odds function, the density function of order statistics, stochastically ordering, and the entropies. The maximum likelihood method is used for model parameters estimation. Following the same approach suggested by Bagdonavicius and Nikulin (2011), modified chi squared goodness-of-fit tests are constructed for right censored data and some tests for right data is considered. An application study is presented to illustrate the ability of the suggested model in fitting aluminum reduction cells sets and the strength data of glass of the aircraft window.
Highlights
Shanker (2017) proposed a distribution of one parameter called as a Rani distribution (RD) with probability density function given by ( ) f RD ( x; ) = 5 5++ x4 e− x, x 0, 0, (1)and the cumulative distribution function of the RD is defined as FRD (x; ) = 1− 1+ x( 3 x3
It is of interest to note here that fTPRD (x;, )dx = 1 and the two parameters Rani distribution (TPRD) reduces to the RD when = 1 . 0
Since the MLE is usually considered for right-censored data, let us consider X1, X2, . . . , Xn be a random right censored sample obtained from the TPRD distribution with the parameter vector = (α, θ)T
Summary
Shanker (2017) proposed a distribution of one parameter called as a Rani distribution (RD) with probability density function (pdf) given by ( ) f. Many authors suggested different new distributions for modeling and fitting various lifetime data in several fields such as medicine, industry, biology, nursing, agriculture, insurance and other fields. These distributions are generated using various methods. The structure of a modified chi-square goodness-of-fit test for the new TPRD when the data are right censored is proposed. For these purposes, we used the criteria tests considered by Bagdonavicius and Nikulin (2011), Bagdonavicius et al (2013).
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