Abstract
A new method for generalizing the Lindley distribution, by increasing the number of mixed models is presented formally. This generalized model, which is called the generalized Lindley of integer order, encompasses the exponential and the usual Lindley distributions as special cases when the order of the model is fixed to be one and two, respectively. The moments, the variance, the moment generating function, and the failure rate function of the initiated model are extracted. Estimation of the underlying parameters by the moment and the maximum likelihood methods are acquired. The maximum likelihood estimation for the right censored data has also been discussed. In a simulation running for various orders and censoring rates, efficiency of the maximum likelihood estimator has been explored. The introduced model has ultimately been fitted to two real data sets to emphasize its application.
Highlights
Lindley [1] distribution has been applied in analyzing lifetime data and stress–strength reliability models, see e.g., Cakmakyapan and Ozel [2]
Lindley distribution which is a mixture of gamma models has attracted the attention of many researchers in recent decades
We introduced a fresh method to generalize the Lindley distribution which the flexibility rises by increasing the number of mixed components in the model
Summary
Lindley [1] distribution has been applied in analyzing lifetime data and stress–strength reliability models, see e.g., Cakmakyapan and Ozel [2]. Symmetry 2020, 12, 1678 have introduced two forms of Lindley generalization by using Lindley with the usual weights p = 1+θ θ and 1 − p and larger value of the underlying shape parameter. Many authors improved the flexibility of the Lindley model by increasing the number of parameters. Broderick and Tiantian [21] proposed a generalized Lindley distribution with four parameters. In this paper, a different idea is introduced based on a two-parameter model but applying additional baseline distributions to gain more flexibility. The proposed model has been fitted to some real-life data that have been already studied in the literature for other models
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