Abstract
In this paper, we introduce a modification of the Quasi Lindley distribution which has various advantageous properties for the lifetime data. Several fundamental structural properties of the distribution are explored. Its density function can be left-skewed, symmetrical, and right-skewed shapes with various rages of tail-weights and dispersions. The failure rate function of the new distribution has the flexibility to be increasing, decreasing, constant, and bathtub shapes. A simulation study is done to examine the performance of maximum likelihood and moment estimation methods in its unknown parameter estimations based on the asymptotic theory. The potentiality of the new distribution is illustrated by means of applications to the simulated and three real-world data sets.
Highlights
The modeling of the lifetime data is a crucial one in many applied sciences, especially engineering, actuarial science, medicine, and others
We have introduced a new three-parameter Lindley family distribution, called the modified Quasi Lindley distribution (MQLD)
We studied its’ fundamental structural properties such as the density, moments and related measures, quantile function, order statistics, failure rate function, mean residual life function, inequality and entropy measures, and size-biased of MQLD
Summary
The modeling of the lifetime data is a crucial one in many applied sciences, especially engineering, actuarial science, medicine, and others. Equation (2) presents two-component mixture of an exponential ( θ ), and gamma ( 2,θ ) with the mixing proportion, p α α +1 It has the increasing failure rate and its skewness ( γ1Q ), kurtosis ( γ 2Q ), and Fano factor ( γ 3Q ) functions are:. Tharshan and Wijekoon (2020) [12] have done a comparison study by introducing a new five-parameter generalized Lindley distribution (FPGLD) They have shown that QLD can perform well than some other existing Lindley family distributions for higher SK, EK, and FF values by using the simulated and real-world data sets. FPGLD ( θ , β = 0,α ,δ ,η ) means FPGLD by setting its location parameter β = 0 This comparison study will be helpful to define the mixing proportion of MQLD that provides a better fit without having additional shape parameter(s) in the new distribution. A simulation study is performed to verify the asymptotic property of unknown parameter estimation methods, and simulated and real-world data sets are used to illustrate its applicability over some other existing Lindley family distributions
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