Goodness-of-fit test for the logistic distribution based on multiply type-II censored samples

Kang, Suk‐Bok; Han, Jun-Tae; Cho, Young-Seuk

doi:10.7465/jkdi.2014.25.1.195

Cited by 5 publications

(6 citation statements)

References 25 publications

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“…For this data set, Kang et al (2010) indicated that the two-parameter half logistic distribution provides a satisfactory fit. In this example, we assume that the underlying distribution of this data is the half-logistic distribution based on the multiply Type I hybrid censoring scheme (i.e.,n = 12, T = 100, r = 11, and a i = 1 ∼ 3, 6 ∼ 12).…”

Section: Real Datamentioning

confidence: 94%

Estimation of the half-logistic distribution based on multiply Type I hybrid censored sample

Shin¹,

Kim²,

Lee³

2014

Journal of the Korean Data and Information Science Society

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In this paper, we consider maximum likelihood estimators of the location and scale parameters for the half-logistic distribution when samples are multiply Type I hybrid censored. The scale parameter is estimated by approximate maximum likelihood estimation methods using two different Taylor series expansion types (σI,σII). We compare the estimators in the sense of the root mean square error (RMSE). The simulation procedure is repeated 10,000 times for the sample size n=20 and 40 and various censored schemes. The approximate MLE of the second type is better than that of the first type in the sense of the RMSE. Further an illustrative example with the real data is presented.

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Section: Real Datamentioning

confidence: 94%

Estimation of the half-logistic distribution based on multiply Type I hybrid censored sample

Shin¹,

Kim²,

Lee³

2014

Journal of the Korean Data and Information Science Society

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“…Based on a gradually type-II censored sample, Wang (2008) provided an exact confidence interval and an exact test for the scale parameter of the HL distribution. Kang and Park (2005) used several type-II censored samples to construct AMLEs of this scale parameter. Adatia (1997) gave an approximation of the size and location parameters of the HL distribution based on a few order statistics such as (k) for reasonably large doubly censored samples.…”

Section: Hl and Related Contributionsmentioning

confidence: 99%

On the Type-I Half-logistic Distribution and Related Contributions: A Review

Muhammad,

Tahir,

Liu

et al. 2023

AJS

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The half-logistic (HL) distribution is a widely considered statistical model for studying lifetime phenomena arising in science, engineering, finance, and biomedical sciences. One of its weaknesses is that it has a decreasing probability density function and an increasing hazard rate function only. Due to that, researchers have been modifying the HL distribution to have more functional ability. This article provides an extensive overview of the HL distribution and its generalization (or extensions). The recent advancements regarding the HL distribution have led to numerous results in modern theory and statistical computing techniques across science and engineering. This work extended the body of literature in a summarized way to clarify some of the states of knowledge, potentials, and important roles played by the HL distribution and related models in probability theory and statistical studies in various areas and applications. In particular, at least sixty-seven flexible extensions of the HL distribution have been proposed in the past few years. We give a brief introduction to these distributions, emphasizing model parameters, properties derived, and the estimation method. Conclusively, there is no doubt that this summary could create a consensus between various related results in both theory and applications of the HL-related models to develop an interest in future studies.

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“…Over several decades, various tests including goodness-of-fit test (Kang et al, 2014;Lee, 2013) using different sources of information from data have been introduced by many researchers. More specifically, some methods exploit sample skewness or/and sample kurtosis (D'Agostino, 1970;D'Agostino and Pearson, 1973;Jarque and Bera, 1981) while other methods use the maximum distance between two distribution functions, i.e., target normal distribution function and empirical distribution function (Kolmogorov, 1933;Lilliefors, 1967Lilliefors, , 1969Smirnov, 1939).…”

Section: Introductionmentioning

confidence: 99%

Comprehensive comparison of normality tests: Empirical study using many different types of data

Lee¹,

Park²,

Jeong³

2016

Journal of the Korean Data and Information Science Society

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We compare many normality tests consisting of different sources of information extracted from the given data: Anderson-Darling test, Kolmogorov-Smirnov test, Cramervon Mises test, Shapiro-Wilk test, Shaprio-Francia test, Lilliefors, Jarque-Bera test, D'Agostino' D, Doornik-Hansen test, Energy test and Martinzez-Iglewicz test. For the purpose of comparison, those tests are applied to the various types of data generated from skewed distribution, unsymmetric distribution, and distribution with different length of support. We then summarize comparison results in terms of two things: type I error control and power. The selection of the best test depends on the shape of the distribution of the data, implying that there is no test which is the most powerful for all distributions.Keywords: Empirical power, empirical type I error, limiting distribution, normality tests. IntroductionMany statistical methodologies, which have been developed so far, work very well under the assumption that the data come from normal distribution and it is very important to check for normality before any statistical analysis is done. Over several decades, various tests including goodness-of-fit test (Kang et al., 2014;Lee, 2013) using different sources of information from data have been introduced by many researchers. More specifically, some methods exploit sample skewness or/and sample kurtosis (D'Agostino, 1970;D'Agostino and Pearson, 1973;Jarque and Bera, 1981) while other methods use the maximum distance between two distribution functions, i.e., target normal distribution function and empirical distribution function (Kolmogorov, 1933;Lilliefors, 1967Lilliefors, , 1969Smirnov, 1939). Other than that, some method uses the ratio of two estimators of variance (Martinez and Iglewicz, 1981 (Anderson, 1962;Cramer, 1928;von Mises, 1928;Shapiro and Wilk, 1965;Shapiro and Francia, 1972;Lilliefors, 1967;Jarque and Bera, 1981;D'Agostino, 1970;Doornik and Hansen, 2008;Szekely and Rizzo, 2005;Martinez and Iglewicz, 1981). Since each method makes use of different type of information extracted from the given data, the performance of each method depends heavily on the properties of the data: skewness, kurtosis, and the type of support. Accordingly, it is well known that there is no test which is the most powerful for all types of alternatives. In order to compare such methods, we apply those tests to the data generated from many different distributions and then find the best test for each alternative.In this paper, we focus on the one sample test. That is, given the samples X 1 , · · · , X n , we test for the normality of the given sample of data. Furthermore, for simplicity, our interest is restricted to the univariate normal data.

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Goodness-of-fit test for the logistic distribution based on multiply type-II censored samples

Cited by 5 publications

References 25 publications

Estimation of the half-logistic distribution based on multiply Type I hybrid censored sample

Estimation of the half-logistic distribution based on multiply Type I hybrid censored sample

On the Type-I Half-logistic Distribution and Related Contributions: A Review

Comprehensive comparison of normality tests: Empirical study using many different types of data

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