Abstract
In recent years, several statistical finite mixture models have been proposed to model the lifetime data with heterogeneity. The Lindley distribution has been highlighted by many authors for these types of lifetime data analysis. This paper introduces a new Lindley family distribution called location-based generalized Akash distribution (NGAD) with monotonic increasing and bathtub failure rates. The density function of NGAD is flexible to cover the left-skewed, right-skewed and symmetrical shapes with different tail-weights. Its fundamental structural properties and its ability to provide a suitable statistical model for various types of data sets are studied. The maximum likelihood (ML) method is used to estimate its unknown parameters and the performance of ML estimates are examined by a simulation study. Finally, several real-data sets with different characteristics are used to illustrate its flexibility. It is observed that NGAD provides a better fit than some other existing modified Lindley distributions.
Highlights
Several standard base-line distributions are available to model the lifetime data and the failure rate function is considered as the most crucial factor for these models
We can measure the tailheaviness of a data set by the excess kurtosis (EK) that is defined as γ − 3, where γ is the kurtosis of the data set
A simulation study is done to study the performance of the maximum likelihood estimators for NGAD, and real-world applications are used to illustrate its flexibility with the above-mentioned existing modified Lindley distributions
Summary
Several standard base-line distributions are available to model the lifetime data and the failure rate function is considered as the most crucial factor for these models. Examples of such distributions are exponential, gamma, Weibull, and log-normal distributions which have different capabilities to describe the shapes of the failure rate function. Time to achieve pain relief in a patient after who has applied with a treatment method does not start from the value of zero In this application, the location parameter of the relevant distribution cannot be taken as zero
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