• 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.

• 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.

• Journal of the Korean Data and Information Science Society
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• v.16 no.1
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• pp.145-156
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• 2005

In this paper, we derive the approximate maximum likelihood estimators (AMLEs) of the scale parameter of the half-logistic distribution based on multiply Type-II censored samples. We compare the proposed estimators in the sense of the mean squared error (MSE) for various censored samples.

• Journal of the Korean Data and Information Science Society
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• v.22 no.5
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• pp.977-989
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• 2011

The half logistic distribution has been used intensively in reliability and survival analysis especially when the data is censored. In this paper, we provide Bayesian estimation of the shape parameter and reliability function in the generalized half logistic distribution based on progressively Type-II censored data under various loss functions. We here consider conjugate prior and noninformative prior and corresponding posterior distributions are obtained. As an illustration, we examine the validity of our estimation using real data and simulated data.

• Journal of the Korean Data and Information Science Society
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• v.22 no.3
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• pp.597-603
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• 2011

The half logistic distribution has been used intensively in reliability and survival analysis especially when the data is censored. In this paper, we provide prole likelihood estimation of the shape parameter and scale parameter in the generalized half logistic distribution based on progressively Type-II censored data. We also introduce approximate maximum prole likelihood estimates for the scale parameter. As an illustration, we examine the validity of our estimation using real data and simulated data.

• 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.

• Journal of Korea Society of Digital Industry and Information Management
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• v.9 no.2
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• pp.1-10
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• 2013

In this paper, make a study decision problem called an optimal release policies after testing a software system in development phase and transfer it to the user. In the course of correcting or modifying the software, finite failure non-homogeneous Poisson process model, presented and was proposed release policies of the life distribution, half-logistic and log-logistic distributions model which used to an area of reliability because of various shape and scale parameter. In this paper, discuss optimal software release policies which minimize a total average software cost of development and maintenance under the constraint of satisfying a software reliability requirement. In a numerical example, the parameter estimation using maximum likelihood estimation of failure time data make out, and software optimal release time was estimated.

• Communications for Statistical Applications and Methods
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• v.31 no.4
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• pp.409-425
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• 2024

Logistic regression models are commonly used to explain binary health outcome variable using independent variables such as patient characteristics in medical science and public health research. Although there is no distributional assumption required for independent variables in logistic regression, variables with severely right-skewed distribution such as lab values are often log-transformed to achieve symmetry or approximate normality. However, lab values often have zeros due to limit of detection which makes it impossible to apply log-transformation. Therefore, preprocessing to handle zeros in the observation before log-transformation is necessary. In this study, five methods that remove zeros (shift by 1, shift by half of the smallest nonzero, shift by square root of the smallest nonzero, replace zeros with half of the smallest nonzero, replace zeros with the square root of the smallest nonzero) are investigated in logistic regression setting. To evaluate performances of these methods, we performed a simulation study based on randomly generated data from log-normal distribution and logistic regression model. Shift by 1 method has the worst performance, and overall shift by half of the smallest nonzero method, replace zeros with half of the smallest nonzero method, and replace zeros with the square root of the smallest nonzero method showed comparable and stable performances.

• 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.

• Communications for Statistical Applications and Methods
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• v.15 no.6
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• pp.815-823
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• 2008

In this paper, we derive the approximate maximum likelihood estimators(AMLEs) and maximum likelihood estimator of the scale parameter in a half-logistic distribution based on progressive Type-II censored samples. We compare the proposed estimators in the sense of the mean squared error for various censored samples. We also obtain the approximate maximum likelihood estimators of the reliability function using the proposed estimators. We compare the proposed estimators in the sense of the mean squared error.