On Sum and Geometric Sum of independent New Quasi Lindley Random Variables and its Applications

Abstract

The Laplace transformation method is used to drive the distribution of the sum Sn of n-fixed random variables, which has a new quasi Lindley distribution with two parameters θ and α, NQLD (θ,α). The sum of NQLD (SUNQLD) distribution is obtained in pdf and cdf formats. It is discussed how to calculate the random sum SN of a random number of NQLD random variables. The random sum of the NQLD distribution's pdf and cdf are calculated. When N has a geometric distribution, the geometric sum of NQLD distribution (GSN QLD) was introduced as an example of a random number of NQLD random variables. For all cases, some statistical measures are determined. The distribution's parameters are estimated using the maximum likelihood method. To test the viability and efficiency of the proposed distributions SNQLD and GSNQLD, lifetime count data sets from acute myeloid leukaemia are fitted. The results should become accepted knowledge in the fields of probability theory and its allied sciences. In addition, the histogram, fitted probability density function (pdf), and P-P plots for the analyzed real data set are presented.