Sum of independent random variable for Shanker, Akash, Ishita, Pranav, Rani and Ram Awadh distributions
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 problemsolving methods are applied which is based on the changeofvariables 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.
 Publication:

arXiv eprints
 Pub Date:
 August 2022
 arXiv:
 arXiv:2208.08006
 Bibcode:
 2022arXiv220808006Y
 Keywords:

 Mathematics  Probability;
 Mathematics  Statistics Theory
 EPrint:
 The manuscript consists of 15 pages, 1 figure and 4 tables