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A comparison study on a new five-parameter generalized Lindley distribution with its sub-models

100%
Tharshan R., Wijekoon P.
Statistics in Transition new series
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2020
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vol. 21
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issue 2
89-117
EN
In recent years, modifications of the classical Lindley distribution have been considered by many authors. In this paper, we introduce a new generalization of the Lindley distribution based on a mixture of exponential and gamma distributions with different mixing proportions and compare its performance with its sub-models. The new distribution accommodates the classical Lindley, Quasi Lindley, Two-parameter Lindley, Shanker, Lindley distribution with location parameter, and Three-parameter Lindley distributions as special cases. Various structural properties of the new distribution are discussed and the size-biased and the lengthbiased are derived. A simulation study is conducted to examine the mean square error for the parameters by means of the method of maximum likelihood. Finally, simulation studies and some real-world data sets are used to illustrate its flexibility in terms of its location, scale and shape parameters.
2
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Odd log-logistic generalised Lindley distribution with properties and applications

88%
Ranjbar V., Eftekharian A., Kharazmi O., Alizadeh M.
Statistics in Transition new series
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2023
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vol. 24
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issue 4
71-92
EN
In this paper, a new three-parameter lifetime model, called the odd log-logistic generalised Lindley distribution, is introduced. Some structural properties of the new distribution including ordinary and incomplete moments, quantile and generating functions and order statistics are obtained. The new density function can be expressed as a linear mixture of exponentiated Lindley densities. Different methods are discussed to estimate the model parameters and a simulation study is carried out to show the performance of the new distribution. The importance and flexibility of the new model are also illustrated empirically by means of two real data sets. Finally, Bayesian analysis and Gibbs sampling are performed based on the two real data sets.
3
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Sujatha Distribution and its Applications

75%
Shanker R.
Statistics in Transition new series
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2016
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vol. 17
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issue 3
391-410
EN
In this paper a new one-parameter lifetime distribution named “Sujatha Distribution” with an increasing hazard rate for modelling lifetime data has been suggested. Its first four moments about origin and moments about mean have been obtained and expressions for coefficient of variation, skewness, kurtosis and index of dispersion have been given. Various mathematical and statistical properties of the proposed distribution including its hazard rate function, mean residual life function, stochastic ordering, mean deviations, Bonferroni and Lorenz curves, and stress-strength reliability have been discussed. Estimation of its parameter has been discussed using the method of maximum likelihood and the method of moments. The applications and goodness of fit of the distribution have been discussed with three real lifetime data sets and the fit has been compared with one-parameter lifetime distributions including Akash, Shanker, Lindley and exponential distributions.
4
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New polynomial exponential distribution: properties and applications

75%
Beghriche A., Zeghdoudi H., Raman V., Chouia S.
Statistics in Transition new series
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2022
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vol. 23
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issue 3
95-112
EN
The study describes the general concept of the XLindley distribution. Forms of density and hazard rate functions are investigated. Moreover, precise formulations for several numerical properties of distributions are derived. Extreme order statistics are established using stochastic ordering, the moment method, the maximum likelihood estimation, entropies and the limiting distribution. We demonstrate the new family's adaptability by applying it to a variety of real-world datasets.
5
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On the characterisation of X-Lindley distribution by truncated moments. Properties and application

75%
METIRI F., ZEGHDOUDI H., EZZEBSA A.
Operations Research and Decisions
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2022
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vol. 32
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issue 1
97-109
EN
This paper presents the characterisation of X-Lindley distribution using the relation between truncated moment and failure rate/reverse failure rate function. An application of this distribution to real data of survival times (in days) of 92 Algerian individuals infected with coronavirus is given.
6
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A Two-Parameter Lindley Distribution

75%
Shanker R., Mishra A.
Statistics in Transition new series
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2013
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vol. 14
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issue 1
45-56
EN
A two-parameter Lindley distribution, of which the Lindley distribution (LD) is a particular case, has been introduced. Its moments, failure rate function, mean residual life function and stochastic orderings have been discussed. The maximum likelihood method and the method of moments have been discussed for estimating its parameters. The distribution has been fitted to some data-sets to test its goodness of fit.
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