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Type II Topp-Leone Frechet distribution: properties and applications

100%
Shanker R., Rahman U. H.
Statistics in Transition new series
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2021
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vol. 22
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issue 4
139-152
EN
The paper focuses on type II Topp-Leone Frechet distribution. Its properties including hazard rate function, reverse hazard rate function, Mills ratio, quantile function and order statistics have been studied. The maximum likelihood estimation used for estimating the parameters of the proposed distribution has been explained and expressions for the Fisher information matrix and confidence intervals have been provided. The paper discusses the applications of the distribution for modeling several datasets relating to temperature. Finally, the goodness of fit of the proposed distribution has been compared with that of the Frechet distribution.
2
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Generalised Odd Frechet Family of Distributions: Properties and Applications

88%
Marganpoor S., Ranjbar V., Alizadeh M., Abdollahnezhad K.
Statistics in Transition new series
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2020
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vol. 21
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issue 3
109-128
EN
A new distribution called Generalized Odd Fréchet (GOF) distribution is presented and its properties explored. Some structural properties of the proposed distribution, including the shapes of the hazard rate function, moments, conditional moments, moment generating function, skewness, and kurtosis are presented. Mean deviations, Lorenz and Bonferroni curves, Rényi entropy, and the distribution of order statistics are given. The maximum likelihood estimation technique is used to estimate the model parameters, and finally applications of the model to a real data set are presented to illustrate the usefulness of the proposed distribution.
3
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Ocena ryzyka zagrożenia powodziowego na rzece Nysa Kłodzka z wykorzystaniem wybranych rozkładów prawdopodobieństwa wartości ekstremalnych

88%
Kuźmiński Ł.
Econometrics. Ekonometria. Advances in Applied Data Analytics
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2016
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issue 1 (51)
48-60
EN
The article concerns the application of selected distributions of extreme values to estimate the risk of occurring of flood danger in Lower Silesia. In the study a daily water level on the Nysa Klodzka River was used, that was gathered in the hydrological station in Bystrzyca Klodzka. From the collected data from the period 1981-2013 biannual maximum water level was selected. Two theoretical distributions: Gumbel and Frechet were fitted to the empirical distribution of biannual maximal. The best fitted two distributions were used for the exemplary assessment of flood danger.
4
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Analysis of COVID-19 and cancer data using new half-logistic generated family of distributions

88%
Khan S., Tahir M. H., Jamal F.
Operations Research and Decisions
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2023
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vol. 33
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issue 4
EN
We focus on a specific sub-model of the proposed family that we call the new half logistic-Fréchet. This sub-model stems from a new generalisation of the half-logistic distribution which we call the new half-logistic-G. The novelty of proposing this new family is that it does not include any additional parameters and instead relies on the baseline parameter. Standard statistical formulas are used to show the forms of the density and failure rate functions, ordinary and incomplete moments with generating functions, and random variate generation. The maximum likelihood estimation procedure is used to estimate the set of parameters. We conduct a simulation analysis to ensure that our calculations are converging with lower mean square error and biases. We use three real-life data sets to equate our model to well-established existing models. The proposed model outperforms the well-established four parameters beta Fréchet and exponentiated generalized Fréchet for some real- -life results, with three parameters such as half-logistic Fréchet, exponentiated Fréchet, Zografos–Balakrishnan gamma Fréchet, Topp–Leonne Fréchet, and Marshall–Olkin Fréchet and two-parameter classical Fréchet distribution.
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