In statistics, data is expressed as a frequency distribution
function that displays the range of potential values for a variable together
with its frequency. Not all real data sets can be well-fitted by standard
probability distributions. Such type of data sets creates a necessity for
developing a new class of flexible probability distributions. To efficiently
model lifetime data, this study develops a novel continuous probability
distribution by building a finite combination of the exponential and Rayleigh
distributions. Compared to current mixing models, the new distribution exhibits
better performance and increases flexibility. The important distributional
features derived include the probability density function (PDF), cumulative
distribution function (CDF), and several statistical properties such as
moments, incomplete moments, survival and hazard functions, mean residual life,
stochastic ordering, order statistics, and stress strength reliability. To
assess inequality and concentration, the Lorenz curve and Bonferroni index are
also obtained. The maximum likelihood method is employed for parameterm
estimation. An empirical study using real data further demonstrates the
applicability and effectiveness of the proposed model.
Author(s) Details
Vidhya G
Department of Mathematics, Rathinam College of Arts and Science,
Coimbatore- 641021, Tamil Nadu, India.
Please see the book here:- https://doi.org/10.9734/bpi/mcsru/v6/5648
