The Hamza Distribution with Statistical Properties and Applications
Ahmad Aijaz *
Department of Mathematics, Bhagwant University, Ajmer, India.
Muzamil Jallal
Department of Mathematics, Bhagwant University, Ajmer, India.
S. Qurat Ul Ain
Department of Mathematics, Bhagwant University, Ajmer, India.
Rajnee Tripathi
Department of Mathematics, Bhagwant University, Ajmer, India.
*Author to whom correspondence should be addressed.
Abstract
This paper suggested a new two parameter distribution named as Hamza distribution. A detailed description about the properties of a suggested distribution including moments, moment generating function, deviations about mean and median, stochastic orderings, Bonferroni and Lorenz curves, Renyi entropy, order statistics, hazard rate function and mean residual function has been discussed. The behavior of a probability density function (p.d.f) and cumulative distribution function (c.d.f) have been depicted through graphs. The parameters of the distribution are estimated by the known method of maximum likelihood estimation. The performance of the established distribution have been illustrated through applications, by which we conclude that the established distribution provide better fit.
Keywords: Moments, moment generating function, reliability measures, mean deviations, maximum likelihood function.