Abstract
In this paper, we introduce a new two-parameter distribution which is called new Odd Log-Logistic Half-Logistic (NOLL-HL) distribution. Theoretical properties of this model including the hazard function, survival function, asymptotic, extreme value, quantile function, moments, conditional moments, mean residual life, mean past lifetime, coefficients of skewness and kurtosis, entropy and order statistics are derived and studied in details. The maximum likelihood estimates of parameters are compared with various methods of estimations by conducting a simulation study. Finally, two real data sets are illustration the purposes
Highlights
Modeling and analyzing lifetime data are important aspects of statistical research in many applied sciences such as engineering, medicine, economics
In many reliability problems, it is of interest to consider variables of the kind (x − X|X ≤ x) for fixed x, called the past lifetime, which denotes the time elapsed after failure till time x given that the unit has already failed by time x defined for a nonnegative random variable X
We introduce a new two-parameter extension of half-logiostic distributions called the new odd log-logistic halflogistic (NOLL-HL) family
Summary
Modeling and analyzing lifetime data are important aspects of statistical research in many applied sciences such as engineering, medicine, economics. Gleaton and Lynch [11] defined a new transformation of distribution function called the odd log-logistic-G (OLLG) family with one additional shape parameter α > 0 by the cdf. If we are interested in modeling the randomness of the odds by the log-logistic pdf r(y) = α yα−1/(1 + yα) (for y > 0), the cdf of Y is given by W [G(x)] be a function of the cdf of a random variable X such that W [G(x)] satisfies the following conditions:. Cdf (8), is called new odd log-logistic half-logistic distribution and denoted by X ∼NOLL-HL(, α, β). These properties include asymptotics, extreme value, mixture for cdf and pdf, moments, conditional moments, mean residual (past) lifetime, mean deviations, Lorenz and Bonferroni curves, entropies and order statistics.
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