Kolmogorov-type tests of goodness-of-fit against stochastic ordering

1997 ◽  
Vol 26 (4) ◽  
pp. 885-897 ◽  
Author(s):  
Kangkyun Kim ◽  
Robert V. Foutz
Keyword(s):  
Goodness Of Fit ◽  
Stochastic Ordering ◽  
Kolmogorov Type

scholarly journals Statistical Inference of the Half-Logistic Inverse Rayleigh Distribution

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 449 ◽  
Author(s):  
Abdullah M. Almarashi ◽  
Majdah M. Badr ◽  
Mohammed Elgarhy ◽  
Farrukh Jamal ◽  
Christophe Chesneau
Keyword(s):  
Statistical Inference ◽  
Goodness Of Fit ◽  
Stochastic Ordering ◽  
Linear Representation ◽  
Rayleigh Distribution ◽  
Model Parameters ◽  
Data Sets ◽  
New Model ◽  
Entropy Measures ◽  
Lifetime Studies

The inverse Rayleigh distribution finds applications in many lifetime studies, but has not enough overall flexibility to model lifetime phenomena where moderately right-skewed or near symmetrical data are observed. This paper proposes a solution by introducing a new two-parameter extension of this distribution through the use of the half-logistic transformation. The first contribution is theoretical: we provide a comprehensive account of its mathematical properties, specifically stochastic ordering results, a general linear representation for the exponentiated probability density function, raw/inverted moments, incomplete moments, skewness, kurtosis, and entropy measures. Evidences show that the related model can accommodate the treatment of lifetime data with different right-skewed features, so far beyond the possibility of the former inverse Rayleigh model. We illustrate this aspect by exploring the statistical inference of the new model. Five classical different methods for the estimation of the model parameters are employed, with a simulation study comparing the numerical behavior of the different estimates. The estimation of entropy measures is also discussed numerically. Finally, two practical data sets are used as application to attest of the usefulness of the new model, with favorable goodness-of-fit results in comparison to three recent extended inverse Rayleigh models.

scholarly journals More powerful goodness-of-fit tests for uniform stochastic ordering

2020 ◽  
Vol 144 ◽  
pp. 106898
Author(s):  
Dewei Wang ◽  
Chuan-Fa Tang ◽  
Joshua M. Tebbs
Keyword(s):  
Goodness Of Fit ◽  
Stochastic Ordering ◽  
Goodness Of Fit Tests

Goodness-of-fit test for uniform stochastic ordering among several distributions

1998 ◽  
Vol 26 (1) ◽  
pp. 69-81 ◽  
Author(s):  
Chul Gyu Park ◽  
Chu-In Charles Lee ◽  
Tim Robertson
Keyword(s):  
Goodness Of Fit ◽  
Stochastic Ordering ◽  
Goodness Of Fit Test

scholarly journals Nonparametric goodness-of-fit tests for uniform stochastic ordering

2017 ◽  
Vol 45 (6) ◽  
pp. 2565-2589 ◽  
Author(s):  
Chuan-Fa Tang ◽  
Dewei Wang ◽  
Joshua M. Tebbs
Keyword(s):  
Goodness Of Fit ◽  
Stochastic Ordering ◽  
Goodness Of Fit Tests

scholarly journals A Two-parameter Rama Distribution

2019 ◽  
pp. 365-382
Author(s):  
U. Umeh Edith ◽  
T. Umeokeke Ebele ◽  
A. Ibenegbu Henrietta
Keyword(s):  
Goodness Of Fit ◽  
Residual Life ◽  
Real Life ◽  
Stochastic Ordering ◽  
Rate Function ◽  
Mean Deviation ◽  
Mean Residual Life ◽  
Estimation Of Parameters ◽  
Lorenz Curves ◽  
Two Parameter

In this paper, a two-parameter Rama distribution is proposed. This is coined from Lindley distribution and Rama distribution. Its mathematical and statistical properties which include its shapes, moment, coefficient of variation, skewness, kurtosis, index of dispersion, hazard rate function, mean residual life function, stochastic ordering, mean deviation; Bonferroni and Lorenz curves are also discussed. The estimation of parameters has been X-rayed using methods of moment and maximum likelihood. Also AIC and BIC are used to test for the goodness of fit of the model which is applied to a real life data of hepatitis B patients. This new distribution is compared with Rama, 2-parameter Akash, 2-parameter Lindley, Akash, Shanker, Ishita, Lindley and Exponential distributions in order to determine the efficiency of the new model.

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