A Characterization and Recurrence Relations of Moments of the Size-Biased Power Function Distribution by Lower Record Values

Shakila Bashir,Mujahid Rasul

doi:10.5539/ijsp.v7n5p1

Abstract

A variety of research papers have been published on record values from various continuous distributions. This paper investigated lower record values from the size-biased power function distribution (LR-SPFD). Some basic properties including moments, skewness, kurtosis, Shannon entropy, cumulative distribution function, survival function and hazard function of the lower record values from SPFD have been discussed. The joint probability density function (pdf) of $n^{th}$ and $m^{th}$ lower record values from SPFD is developed. Recurrence relations of the single and product moments of the LR-SPFD have been derived. A characterization of the lower record values from SPFD is also developed.

Highlights

In the environmental and ecological work, observations usually fall in the non-experimental, non-replicated, and nonrandom categories
This paper investigated lower record values from the size-biased power function distribution (LR-SPFD)
And Figure 1, 2&3 it can be concluded that the shape of the LR-SPFD is approaching to symmetric for β ≥ 5, n ≥ 5

Summary

Introduction

In the environmental and ecological work, observations usually fall in the non-experimental, non-replicated, and nonrandom categories. In this article we are introducing the lower record values from size-biased power function distribution (SPFD). Recurrence relations for single and product moments, a characterization of the lower record values from SPFD are discussed. Ahsanullah (2010) derived the rth concomitants and joint distribution of rth and sth concomitants of record values from the bivariate pseudo-Weibull distribution He derived recurrence relation for the single moments. Bashir and Ahmad (2015) developed recurrence relations for single and product moments of record values from size-biased Pareto distribution. Saran and Pandey (2004) developed recurrence relations for moments, characterization and estimated parameters of a power function distribution by kth record values. Ahsanullah, et al (2013) provided a new characterization of power function distribution based on lower record values. The mth moments of the power function distribution is μ′m βαm (m + β)

Record Values from the Size-Biased Power Function Distribution

Moments

Recurrence Relations for Moments

Conclusion