On Poisson-Akash Distribution and its Applications

Abstract

In this paper a simple and interesting method for finding moments of Poisson-Akash distribution (PAD) introduced by Shanker [1] has been suggested and hence the first two moments

Rani Distribution and Its Application

“…In this section, the goodness of fit of Rani distribution has been discussed with a real lifetime data set from engineering and the fit has been compared with one parameter lifetime distributions namely Akash [3], Shanker [4], Amarendra [7], Aradhana [5], Sujatha [6], Devya [8], Lindley [1] and exponential. The data set is the strength data of glass of the aircraft window reported by Fuller, et al [14] The formulae for computing AIC and K-S Statistic are as follows: Table (4).…”

“…The data set is the strength data of glass of the aircraft window reported by Fuller, et al [14] The formulae for computing AIC and K-S Statistic are as follows: Table (4). It can be easily observed from above Table (3) that Rani distribution gives better fit than the fit given by Akash [3], Rama [9], Akshaya [10], Shanker [4], Amarendra [7], Aradhana [5], Sujatha [6], Devya [8], Lindley [1] and exponential distributions and hence it can be considered as an important lifetime distribution for modeling lifetime data over these distributions.…”

“…Shanker, et al [2] have detailed comparative study on modeling of lifetime data from various fields of knowledge and observed that there are many lifetime data where these two distributions are not suitable due to their shapes, nature of hazard rate functions, and mean residual life functions, amongst others. In search for new one parameter lifetime distributions which gives better fit than exponential and Lindley distributions, recently Shanker has introduced several one parameter lifetime distributions in statistical literature namely Akash [3], Shanker [4], Aradhana [5], Sujatha [6], Amarendra [7], Devya [8], Rama [9] and Akshaya [10] and showed that these distributions gives better fit than the classical exponential and Lindley distributions. The probability density function (pdf) and the corresponding cumulative distribution function (cdf) of Akash [3], Shanker [4], Aradhana [5], Sujatha [6], Amarendra [7], Devya [8], Rama [9] and Lindley [1] distributions are presented in Table (1).…”

“…In search for new one parameter lifetime distributions which gives better fit than exponential and Lindley distributions, recently Shanker has introduced several one parameter lifetime distributions in statistical literature namely Akash [3], Shanker [4], Aradhana [5], Sujatha [6], Amarendra [7], Devya [8], Rama [9] and Akshaya [10] and showed that these distributions gives better fit than the classical exponential and Lindley distributions. The probability density function (pdf) and the corresponding cumulative distribution function (cdf) of Akash [3], Shanker [4], Aradhana [5], Sujatha [6], Amarendra [7], Devya [8], Rama [9] and Lindley [1] distributions are presented in Table (1). It has also been discussed by Shanker that although each of these lifetime distributions has advantages and disadvantages over one another due to its shapes, hazard rate functions and mean residual life functions, there are still many lifetime data where these distributions are not suitable for modeling lifetime data from theoretical or applied point of view.…”

“…Figure (3). The condition under which Rani distribution is over-dispersed, equi-dispersed, and under-dispersed along with condition under which Akash [3], Rama [9], Akshaya [10], Shanker [4], Amarendra [7], Aradhana [5], Sujatha [6], Devya [8], Lindley [1] and exponential distributions are over-dispersed, equi-dispersed, and under-dispersed are presented in Table (2). …”