• Title/Summary/Keyword: exponentiated half logistic distribution

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Estimation in an Exponentiated Half Logistic Distribution under Progressively Type-II Censoring

  • Kang, Suk-Bok;Seo, Jung-In
    • Communications for Statistical Applications and Methods
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    • v.18 no.5
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    • pp.657-666
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    • 2011
  • In this paper, we derive the maximum likelihood estimator(MLE) and some approximate maximum likelihood estimators(AMLEs) of the scale parameter in an exponentiated half logistic distribution based on progressively Type-II censored samples. We compare the proposed estimators in the sense of the mean squared error(MSE) through a Monte Carlo simulation for various censoring schemes. We also obtain the AMLEs of the reliability function.

Bayesian analysis of an exponentiated half-logistic distribution under progressively type-II censoring

  • Kang, Suk Bok;Seo, Jung In;Kim, Yongku
    • Journal of the Korean Data and Information Science Society
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    • v.24 no.6
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    • pp.1455-1464
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    • 2013
  • This paper develops maximum likelihood estimators (MLEs) of unknown parameters in an exponentiated half-logistic distribution based on a progressively type-II censored sample. We obtain approximate confidence intervals for the MLEs by using asymptotic variance and covariance matrices. Using importance sampling, we obtain Bayes estimators and corresponding credible intervals with the highest posterior density and Bayes predictive intervals for unknown parameters based on progressively type-II censored data from an exponentiated half logistic distribution. For illustration purposes, we examine the validity of the proposed estimation method by using real and simulated data.

Estimation of the exponentiated half-logistic distribution based on multiply Type-I hybrid censoring

  • Jeon, Young Eun;Kang, Suk-Bok
    • Communications for Statistical Applications and Methods
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    • v.27 no.1
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    • pp.47-64
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    • 2020
  • In this paper, we derive some estimators of the scale parameter of the exponentiated half-logistic distribution based on the multiply Type-I hybrid censoring scheme. We assume that the shape parameter λ is known. We obtain the maximum likelihood estimator of the scale parameter σ. The scale parameter is estimated by approximating the given likelihood function using two different Taylor series expansions since the likelihood equation is not explicitly solved. We also obtain Bayes estimators using prior distribution. To obtain the Bayes estimators, we use the squared error loss function and general entropy loss function (shape parameter q = -0.5, 1.0). We also derive interval estimation such as the asymptotic confidence interval, the credible interval, and the highest posterior density interval. Finally, we compare the proposed estimators in the sense of the mean squared error through Monte Carlo simulation. The average length of 95% intervals and the corresponding coverage probability are also obtained.

Generalized half-logistic Poisson distributions

  • Muhammad, Mustapha
    • Communications for Statistical Applications and Methods
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    • v.24 no.4
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    • pp.353-365
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    • 2017
  • In this article, we proposed a new three-parameter distribution called generalized half-logistic Poisson distribution with a failure rate function that can be increasing, decreasing or upside-down bathtub-shaped depending on its parameters. The new model extends the half-logistic Poisson distribution and has exponentiated half-logistic as its limiting distribution. A comprehensive mathematical and statistical treatment of the new distribution is provided. We provide an explicit expression for the $r^{th}$ moment, moment generating function, Shannon entropy and $R{\acute{e}}nyi$ entropy. The model parameter estimation was conducted via a maximum likelihood method; in addition, the existence and uniqueness of maximum likelihood estimations are analyzed under potential conditions. Finally, an application of the new distribution to a real dataset shows the flexibility and potentiality of the proposed distribution.