Sum of independent random variable for Shanker, Akash, Ishita, Pranav, Rani and Ram Awadh distributions

TL;DR

This paper derives the probability density functions and moments for the sum of n independent identically distributed random variables from specific named distributions, and evaluates system reliability under Lindley failure times.

Contribution

It introduces the PDFs and moments for sums of these specific distributions and analyzes the reliability of a cold standby system with Lindley failure times.

Findings

Derived PDFs for sums of the distributions.

Calculated moments for the distributions.

Evaluated system reliability and mean time to failure.

Abstract

In statistics and probability theory, one the most important statistics is the sums of random variables. After introducing a probability distribution, determining the sum of n independent and identically distributed random variables is one of the interesting topics for authors. This paper presented the probability density function for the sum of n independent and identically distributed random variables such as Shanker, Akash, Ishita, Rani, Pranav and Ram Awadh. In order to determine all aforementioned distributions, the problem-solving methods are applied which is based on the change-of-variables technique. The mth moments for them were also accurately calculated. Besides, the reliability and the mean time to failure of a 1 out of n cold standby spare system has also been evaluated under the Lindley components failure time.