The Odd Log-Logistic Marshall-Olkin Lindley Model for Lifetime Data

Abstract

A new three parameter model called the odd log-logistic Marshall-Olkin-Lindley (OLLMO-L) distribution is proposed and studied. This distribution is symmetric, platykurtic, leptokurtic and unimodal. Various structural properties are derived, including explicit expressions for the ordinary and conditional moments, generating function and order statistics. We use maximum likelihood method to estimate the parameters of model. Simulation studies for some particular cases are also run to assess the performance of the maximum likelihood estimators. We prove empirically that the proposed distribution is a very competitive model to other classical models by means of two real data sets.

An Extended Lindley Distribution with Application to Lifetime Data with Bayesian Estimation

“…One may be interested in the asymptotic of the extreme values Mn = max(X 1 , ..., Xn) and mn = min(X 1 , ..., Xn). Let τ (x) = 1 λ , we obtain following equations for the cdf in (6) as…”

“…Asgharzadeh et al [10] proposed Weibull Lindley distribution based on three parameters. Recently, using odd log-logistic family and by considering Lindley distribution as underlying distribution several contributions are presented by Alizadeh et al [4], [5] and [6]. Also, we can mention [14] and [16] as other contributions in related to the Lindley distribution.…”

The Lomax-Lindley distribution: properties and applications to lifetime data

“…In this regard, some researchers have considered modified forms and generalizations of these distributions to provide more flexibility for describing different types of data. For example, McDonald Lomax distribution by Lemonte and Cordeiro [14], Weibull-Lomax distribution by Tahir et al [23], Burr X exponentiated Lomax distribution by Aboraya [1], new extended generalized lindley distribution by Maya and Irshad [19], odd log-logistic Lindley distribution by Ozel et al [21], odd log-logistic Marshal-Olkin Lindley distribution by Alizadeh et al [3] and exponentiated power Lindley power series class of distributions by Alizadeh et al [2]. Most of these distributions have four or more parameters which cause estimation problems as a consequence of the number of parameters.…”

A new extended log-Weibull regression: Simulations and applications

“…The extended generalized log-logistic family with two additional parameters is reported by [2] and [11] as the odd-log-logistic Marshall-Olkin-G (OLLMO-G) class. In fact, the OLLMO-G class is the Marshall-Olkin-odd-log-logistic-G (MOOLL-G) family, which follows by inserting (1.2) in Equation (1.1), having cdf (for x ∈ R)…”

“…Remark 1.2. Alizadeh et al [2] investigated some properties of the OLLMO-Lindley and OLLMO-power Lindley models (in fact the MOOLL-Lindley and MOOLL-power Lindley models). Recently, Lima et al [14] studied a variant of the MOOLL-G class, called the OLL-Geometric-G (OLL-Geo-G) family, for a system of components arranged in a series structure, whose cdf takes the form (for x ∈ R)…”