A Generalized Exponential-Lindley Distribution

Mishra, A.; Sah, Binod Kumar

doi:10.1142/9789814704830_0021

Cited by 3 publications

(4 citation statements)

References 6 publications

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“…It can also be seen that at 0 x  , the mean residual life function ( 23) is the mean OPLED (3). It can also be seen that m(x) is a decreasing function of x, The hazard rate function and the mean residual life function of the OPLED show its flexibility over Lindley distribution.…”

Section: Residual Life Functionmentioning

confidence: 84%

“…Where f(x) and F(x) are the probability density function and probability distribution function of OPLED (3).…”

Section: Residual Life Functionmentioning

confidence: 99%

“…Mishra and Sah (2015) [3] obtained a generalised Lindley-exponential distribution which gives better alternative to the Lindley distribution but it has two parameters. So, we think that it is not fare to compare with the distribution having a single parameter.…”

Section: Introductionmentioning

confidence: 99%

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One-parameter linear-exponential distribution

Sah¹

2021

Int. J. Stat. Appl. Math.

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In this paper, we introduce a new continuous probability distribution which is based on the product of linear and exponential functions having a single parameter and hence, we named it 'One-parameter Linear-exponential distribution'. Different structural properties such as probability density function, probability distribution function and moment generating function of this distribution have been derived. Moments about origin and hence, the first four central moments of the proposed distribution have been obtained. The hazard rate function and the mean residual life function of the proposed distribution have been discussed, and show its flexibility over Lindley distribution. Estimation of parameters has been discussed by the method of moments as well as the method of maximum likelihood. Goodness of fit has been applied to different data-sets which were used by others. It has been observed that the proposed distribution gives better fit to the most of data-sets of same nature, having variance greater than the mean, than Lindley distribution.

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Section: Residual Life Functionmentioning

confidence: 84%

“…Where f(x) and F(x) are the probability density function and probability distribution function of OPLED (3).…”

Section: Residual Life Functionmentioning

confidence: 99%

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One-parameter linear-exponential distribution

Sah¹

2021

Int. J. Stat. Appl. Math.

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“…The Lindley distribution was originally proposed by Lindley (1958) in the context of Bayesian Statistics, as a counter example of fiducial Statistics. The exponential and Lindley distributions both are the particular cases of generalised exponential-Lindley distribution (GELD) of Mishra and Sah (2016) and its probability density function (pdf) is given by:…”

Section: Introductionmentioning

confidence: 99%

On a Generalised Exponential-Lindley Mixture of Generalised Poisson Distribution

Sah

Mishra

2020

Nep. J. Stats.

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Background: A mixture distribution arises when some or all parameters in a mixing distribution vary according to the nature of original distribution. A generalised exponential-Lindley distribution (GELD) was obtained by Mishra and Sah (2015). In this paper, generalized exponential- Lindley mixture of generalised Poisson distribution (GELMGPD) has been obtained by mixing generalised Poisson distribution (GPD) of Consul and Jain’s (1973) with GELD. In the proposed distribution, GELD is the original distribution and GPD is a mixing distribution. Generalised exponential- Lindley mixture of Poisson distribution (GELMPD) was obtained by Sah and Mishra (2019). It is a particular case of GELMGPD. Materials and Methods: GELMGPD is a compound distribution obtained by using the theoretical concept of some continuous mixtures of generalised Poisson distribution of Consul and Jain (1973). In this mixing process, GELD plays a role of original distribution and GPD is considered as mixing distribution. Results: Probability mass of function (pmf) and the first four moments about origin of the generalised exponential-Lindley mixture of generalised Poisson distribution have been obtained. The method of moments has been discussed to estimate parameters of the GELMGPD. This distribution has been fitted to a number of discrete data-sets which are negative binomial in nature. P-value of this distribution has been compared to the PLD of Sankaran (1970) and GELMPD of Sah and Mishra (2019) for similar type of data-sets. Conclusion: It is found that P-value of GELMGPD is greater than that in each case of PLD and GELMPD. Hence, it is expected to be a better alternative to the PLD of Sankaran and GELMPD of Sah and Mishra for similar types of discrete data-sets which are negative binomial in nature. It is also observed that GELMGPD gives much more significant result when the value of is negative.

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Lindley Power Series Distributions

Nadarajah

2018

Sankhya A

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A Generalized Exponential-Lindley Distribution

Cited by 3 publications

References 6 publications

One-parameter linear-exponential distribution

One-parameter linear-exponential distribution

On a Generalised Exponential-Lindley Mixture of Generalised Poisson Distribution

Lindley Power Series Distributions

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