New Generalizations of Exponential Distribution with Applications

Rather, N. A.; Rather, Tariq

doi:10.1155/2017/2106748

Cited by 10 publications

(6 citation statements)

References 15 publications

(16 reference statements)

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“…For each pair (n, "), the simulation study was iterated 3000 times. The Erlang parameter values used are (1, 2) and (2,3). For the quasi hyper-parameter values, the following values were assumed: c 1 = 0.5 and c 2 = 1.…”

Section: Simulation and Resultsmentioning

confidence: 99%

“…Such distributions among others include Erlang, normal, poison, negative binomial, Weibull and exponential distributions 1 . An exponential distribution is a special case of the gamma family known for modelling the time interval between two successive Poisson events 2 . Gamma distribution is useful in finding the joint probability distribution of hydrological events (frequency analysis).…”

Section: Introductionmentioning

confidence: 99%

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Classical and Bayesian Methods in Estimation of a Scale Parameter of an Erlang Distribution

Oguntade¹,

Oladimeji²

2023

J. of Applied Sciences

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This study examined the Bayesian and Classical approaches in the estimation of a scale a parameter of an Erlang distribution under different loss functions (both symmetric and asymmetric loss functions) and prior probabilities. The shape parameter was assumed known while the scale parameter was assumed to follow Jeffreyʼs, quasi and uniform priors. A square error loss, entropy loss and linear exponential loss functions were considered. Under different combinations and scenarios of these priors and loss functions, the estimators of the scale parameter of an Erlang distribution were derived using R software. The estimators were compared and the best estimator was chosen based on having the least value of the mean square error of the estimates.

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Section: Simulation and Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Classical and Bayesian Methods in Estimation of a Scale Parameter of an Erlang Distribution

Oguntade¹,

Oladimeji²

2023

J. of Applied Sciences

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“…Although this distribution is very capable of modeling very different kinds of lifetime data sets, in some data sets, the modeling success rate may be lower. In some studies-to fix this situation-researchers add more parameters for better modeling ( [10], [2], [8].…”

Section: Introductionmentioning

confidence: 99%

A new transmutation: conditional copula with exponential distribution

Ünözkan

Yılmaz

2023

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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In these days, many different techniques are implemented for generating distributions. The core aim in generating distribution, is better modeling capability. With generating new distribution more reliable and appropriate models are available for data sets. In this paper, a new distribution is gained by evaluating the conditional diagonal section of the bivariate Farlie-Gumbel-Morgenstern distribution with exponential marginals. Specifications and characteristics of this new distribution are studied. The statistical assessment and some reliability analyzes are carried out. The success of the new distribution on statistical modeling is detected by using data sets in literature. It is concluded that this new distribution suggests a model that can be used effectively in many different lifetime data sets.

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“…Hence, many generalized forms of this distribution came into existence. Some of them are the generalized exponential distributions by Gupta and Kundu [13], the k-generalized exponential distribution proposed by Rather and Rather [25], the extended exponentiated exponential distribution and its properties by Abu et al [2]. Also, numerous lifetime distributions have been proposed as an alternative to exponential distribution for modeling lifetime data in the literature.…”

Section: Introductionmentioning

confidence: 99%

Generalization of the Lindley distribution with application to COVID-19 data

Rajitha

Akhilnath

2022

Int J Data Sci Anal

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Creating new distributions with more desired and flexible qualities for modeling lifetime data has resulted in a concentrated effort to modify or generalize existing distributions. In this paper, we propose a new distribution called the power exponentiated Lindley (PEL) distribution by generalizing the Lindley distribution using the power exponentiated family of distributions, that can fit lifetime data. Then the main statistical properties such as survival function, hazard function, reverse hazard function, moments, quantile function, stochastic ordering, MRL, order statistics, etc., of the newly proposed distribution have been derived. The parameters of the distribution are estimated using the MLE method. Then, a Monte Carlo simulation study is used to check the consistency of the parameters of the PEL distribution in terms of MSE, RMSE, and bias. Finally, we implement the PEL distribution as a statistical lifetime model for the COVID-19 case fatality ratio (in %) in China and India, and the new cases of COVID-19 reported in Delhi. Then we check whether the new distribution fits the data sets better than existing well-known distributions. Different statistical measures such as the value of the log-likelihood function, K-S statistic, AIC, BIC, HQIC, and p -value are used to assess the accuracy of the model. The suggested model seems to be superior to its base model and other well-known and related models when applied to the COVID-19 data set.

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New Generalizations of Exponential Distribution with Applications

Cited by 10 publications

References 15 publications

Classical and Bayesian Methods in Estimation of a Scale Parameter of an Erlang Distribution

Classical and Bayesian Methods in Estimation of a Scale Parameter of an Erlang Distribution

A new transmutation: conditional copula with exponential distribution

Generalization of the Lindley distribution with application to COVID-19 data

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