scholarly journals The transmuted generalized modified Weibull distribution

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1395-1412 ◽  
Author(s):  
Gaussm Cordeiro ◽  
Abdus Saboor ◽  
Muhammad Khan ◽  
Serge Provost
Keyword(s):  
Weibull Distribution ◽  
Goodness Of Fit ◽  
Real Data ◽  
Rate Function ◽  
Modified Weibull Distribution ◽  
Positive Data ◽  
Anderson Darling ◽  
Generalized Modified Weibull ◽  
Modified Weibull ◽  
Von Mises

Canada EM [email protected] AU Ortega Edwinm M. AF Universidade de S?o Paulo, Departamento de Ci?ncias Exatas, Piracicaba, Brazil EM [email protected] KW Generalized modifiedWeibull distribution % Goodness-of-fit statistic % Lifetime data % Transmuted family % Weibull distribution KR nema A profusion of new classes of distributions has recently proven useful to applied statisticians working in various areas of scientific investigation. Generalizing existing distributions by adding shape parameters leads to more flexible models. We define a new lifetime model called the transmuted generalized modified Weibull distribution from the family proposed by Aryal and Tsokos [1], which has a bathtub shaped hazard rate function. Some structural properties of the new model are investigated. The parameters of this distribution are estimated using the maximum likelihood approach. The proposed model turns out to be quite flexible for analyzing positive data. In fact, it can provide better fits than related distributions as measured by the Anderson-Darling (A*) and Cram?r-von Mises (W*) statistics, which is illustrated by applying it to two real data sets. It may serve as a viable alternative to other distributions for modeling positive data arising in several fields of science such as hydrology, biostatistics, meteorology and engineering.

scholarly journals The gamma exponentiated exponential-Weibull distribution

Filomat ◽  
2016 ◽  
Vol 30 (12) ◽  
pp. 3159-3170 ◽  
Author(s):  
Tibor Pogány ◽  
Abdus Saboor
Keyword(s):  
Biological Sciences ◽  
Weibull Distribution ◽  
Goodness Of Fit ◽  
Data Sets ◽  
Fit Statistics ◽  
Positive Data ◽  
Special Cases ◽  
Likelihood Approach ◽  
Anderson Darling ◽  
Von Mises

Anewfour-parameter model called the gamma-exponentiated exponential-Weibull distribution is being introduced in this paper. The new model turns out to be quite flexible for analyzing positive data. Representations of certain statistical functions associated with this distribution are obtained. Some special cases are pointed out as well. The parameters of the proposed distribution are estimated by making use of the maximum likelihood approach. This density function is utilized to model two actual data sets. The new distribution is shown to provide a better fit than related distributions as measured by the Anderson-Darling and Cram?r-von Mises goodness-of-fit statistics. The proposed distribution may serve as a viable alternative to other distributions available in the literature for modeling positive data arising in various fields of scientific investigation such as the physical and biological sciences, hydrology, medicine, meteorology and engineering.

scholarly journals Favorable Estimators for Fitting Pareto Models: A Study Using Goodness-of-fit Measures with Actual Data

2003 ◽  
Vol 33 (2) ◽  
pp. 365-381 ◽  
Author(s):  
Vytaras Brazauskas ◽  
Robert Serfling
Keyword(s):  
Goodness Of Fit ◽  
Real Data ◽  
Efficient Estimation ◽  
Small Samples ◽  
Robust Estimators ◽  
Trade Offs ◽  
Pareto Model ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Von Mises

Several recent papers treated robust and efficient estimation of tail index parameters for (equivalent) Pareto and truncated exponential models, for large and small samples. New robust estimators of “generalized median” (GM) and “trimmed mean” (T) type were introduced and shown to provide more favorable trade-offs between efficiency and robustness than several well-established estimators, including those corresponding to methods of maximum likelihood, quantiles, and percentile matching. Here we investigate performance of the above mentioned estimators on real data and establish — via the use of goodness-of-fit measures — that favorable theoretical properties of the GM and T type estimators translate into an excellent practical performance. Further, we arrive at guidelines for Pareto model diagnostics, testing, and selection of particular robust estimators in practice. Model fits provided by the estimators are ranked and compared on the basis of Kolmogorov-Smirnov, Cramér-von Mises, and Anderson-Darling statistics.

scholarly journals Goodness-of-fit tests for the beta Gompertz distribution

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 69-81
Author(s):  
Hanaa Abu-Zinadah ◽  
Asmaa Binkhamis
Keyword(s):  
Goodness Of Fit ◽  
Real Data ◽  
Likelihood Method ◽  
Test Statistics ◽  
Gompertz Distribution ◽  
Goodness Of Fit Tests ◽  
Lilliefors Test ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Von Mises

This article studied the goodness-of-fit tests for the beta Gompertz distribution with four parameters based on a complete sample. The parameters were estimated by the maximum likelihood method. Critical values were found by Monte Carlo simulation for the modified Kolmogorov-Smirnov, Anderson-Darling, Cramer-von Mises, and Lilliefors test statistics. The power of these test statistics founded the optimal alternative distribution. Real data applications were used as examples for the goodness of fit tests.

scholarly journals Favorable Estimators for Fitting Pareto Models: A Study Using Goodness-of-fit Measures with Actual Data

2003 ◽  
Vol 33 (02) ◽  
pp. 365-381 ◽  
Author(s):  
Vytaras Brazauskas ◽  
Robert Serfling
Keyword(s):  
Goodness Of Fit ◽  
Real Data ◽  
Efficient Estimation ◽  
Small Samples ◽  
Robust Estimators ◽  
Trade Offs ◽  
Pareto Model ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Von Mises

Several recent papers treated robust and efficient estimation of tail index parameters for (equivalent) Pareto and truncated exponential models, for large and small samples. New robust estimators of “generalized median” (GM) and “trimmed mean” (T) type were introduced and shown to provide more favorable trade-offs between efficiency and robustness than several well-established estimators, including those corresponding to methods of maximum likelihood, quantiles, and percentile matching. Here we investigate performance of the above mentioned estimators on real data and establish — via the use of goodness-of-fit measures — that favorable theoretical properties of the GM and T type estimators translate into an excellent practical performance. Further, we arrive at guidelines for Pareto model diagnostics, testing, and selection of particular robust estimators in practice. Model fits provided by the estimators are ranked and compared on the basis of Kolmogorov-Smirnov, Cramér-von Mises, and Anderson-Darling statistics.

A generalized modified Weibull distribution for lifetime modeling

2008 ◽  
Vol 53 (2) ◽  
pp. 450-462 ◽  
Author(s):  
Jalmar M.F. Carrasco ◽  
Edwin M.M. Ortega ◽  
Gauss M. Cordeiro
Keyword(s):  
Weibull Distribution ◽  
Modified Weibull Distribution ◽  
Generalized Modified Weibull ◽  
Modified Weibull
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