scholarly journals Goodness‐of‐fit measures based on the Mellin transform for beta generalized lifetime data

2021 ◽  
Author(s):  
Josimar M. Vasconcelos ◽  
Renato J. Cintra ◽  
Abraão D. C. Nascimento
Keyword(s):  
Goodness Of Fit ◽  
Mellin Transform ◽  
Lifetime Data

scholarly journals Goodness-of-fit Measures Based on the Mellin Transform for Beta Generalized Lifetime Data

2021 ◽  
Author(s):  
Josimar Vasconcelos ◽  
Renato Cintra ◽  
Abraão Nascimento
Keyword(s):  
Goodness Of Fit ◽  
Mellin Transform ◽  
Real Data ◽  
Data Sets ◽  
Lifetime Data ◽  
Probability Models ◽  
Probability Weighted Moments ◽  
Confidence Ellipses ◽  
Heavy Tail Distributions ◽  
Combine Probability

In recent years various probability models have been proposed for describing lifetime data. Increasing model flexibility is often sought as a means to better describe asymmetric and heavy tail distributions. Such extensions were pioneered by the beta-G family. However, efficient goodness-of-fit (GoF) measures for the beta-G distributions are sought. In this paper, we combine probability weighted moments (PWMs) and the Mellin transform (MT) in order to furnish new qualitative and quantitative GoF tools for model selection within the beta-G class. We derive PWMs for the Fr\’{e}chet and Kumaraswamy distributions; and we provide expressions for the MT, and for the log-cumulants (LC) of the beta-Weibull, beta-Fr\’{e}chet, beta-Kumaraswamy, and beta-log-logistic distributions. Subsequently, we construct LC diagrams and, based on the Hotelling’s $T^2$ statistic, we derive confidence ellipses for the LCs. Finally, the proposed GoF measures are applied on five real data sets in order to demonstrate their applicability.

scholarly journals A New Two-Parameter Lindley Distribution

2020 ◽  
Vol 1 ◽  
pp. 33-42
Author(s):  
Rama Shanker ◽  
Umme Habibah Rahman
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Fisher Information Matrix ◽  
Information Matrix ◽  
Likelihood Estimation ◽  
Lifetime Data ◽  
Lindley Distribution ◽  
Method Of Maximum Likelihood ◽  
Two Parameter ◽  
Family Of Distributions

In this paper, a new two-parameter Lindley distribution has been proposed. Descriptive statistical properties along with order statistics, Fisher information matrix and confidence interval of the proposed distribution have been discussed. Parameters are estimated by the method of Maximum Likelihood estimation. A real lifetime data has been presented to test the goodness of fit of the proposed distribution over other one parameter and two –parameter Lindley family of distributions.

The exponentiated exponential burr XII distribution: Theory and application to lifetime data

2020 ◽  
pp. 1-14
Author(s):  
Majdah M. Badr
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Significant Heterogeneity ◽  
Lifetime Data ◽  
Fit Statistics ◽  
Mathematical Properties ◽  
New Distribution

Lifetime data collected from reliability tests are among data that often exhibit significant heterogeneity caused by variations in manufacturing which make standard lifetime models inadequate. In this paper we introduce a new lifetime distribution derived from T-X family technique called exponentiated exponential Burr XII (EE-BXII) distribution. We establish various mathematical properties. The maximum likelihood estimates (MLE) for the EE-BXII parameters are derived. We estimate the precision of the maximum likelihood estimators via simulation study. Some numerical illustrations are performed to study the behavior of the obtained estimators. Finally the model is applied to a real dataset. We apply goodness of fit statistics and graphical tools to examine the adequacy of the EE-BXII distribution. The importance of this research lies in deriving a new distribution under the name EE-BXII, which is considered the best distributions in analyzing data of life times at present if compared to many distributions in analysis real data.

Goodness-of-Fit Tests for Multilook Polarimetric Radar Data Based on the Mellin Transform

2011 ◽  
Vol 49 (7) ◽  
pp. 2764-2781 ◽  
Author(s):  
Stian Normann Anfinsen ◽  
Anthony Paul Doulgeris ◽  
Torbjørn Eltoft
Keyword(s):  
Goodness Of Fit ◽  
Mellin Transform ◽  
Radar Data ◽  
Polarimetric Radar ◽  
Goodness Of Fit Tests

Applying the Anderson-Darling Test to Suicide Clusters

Crisis ◽  
2013 ◽  
Vol 34 (6) ◽  
pp. 434-437 ◽  
Author(s):  
Donald W. MacKenzie
Keyword(s):  
Poisson Process ◽  
Goodness Of Fit ◽  
Small Samples ◽  
Massachusetts Institute Of Technology ◽  
Homogeneous Poisson Process ◽  
Cornell University ◽  
The Difference ◽  
Suicide Clusters ◽  
Institute Of Technology ◽  
Anderson Darling

Background: Suicide clusters at Cornell University and the Massachusetts Institute of Technology (MIT) prompted popular and expert speculation of suicide contagion. However, some clustering is to be expected in any random process. Aim: This work tested whether suicide clusters at these two universities differed significantly from those expected under a homogeneous Poisson process, in which suicides occur randomly and independently of one another. Method: Suicide dates were collected for MIT and Cornell for 1990–2012. The Anderson-Darling statistic was used to test the goodness-of-fit of the intervals between suicides to distribution expected under the Poisson process. Results: Suicides at MIT were consistent with the homogeneous Poisson process, while those at Cornell showed clustering inconsistent with such a process (p = .05). Conclusions: The Anderson-Darling test provides a statistically powerful means to identify suicide clustering in small samples. Practitioners can use this method to test for clustering in relevant communities. The difference in clustering behavior between the two institutions suggests that more institutions should be studied to determine the prevalence of suicide clustering in universities and its causes.

Confirmatory Factor Analysis of the Long and Short Forms of the Worry Domains Questionnaire

2009 ◽  
Vol 25 (4) ◽  
pp. 239-243
Author(s):  
Roberto Nuevo ◽  
Andrés Losada ◽  
María Márquez-González ◽  
Cecilia Peñacoba
Keyword(s):  
Factor Analysis ◽  
Confirmatory Factor Analysis ◽  
Factor Structure ◽  
Goodness Of Fit ◽  
Factorial Validity ◽  
Fit Indices ◽  
Short Forms ◽  
Confirmatory Factor ◽  
Positive Correlations ◽  
Future Work

The Worry Domains Questionnaire was proposed as a measure of both pathological and nonpathological worry, and assesses the frequency of worrying about five different domains: relationships, lack of confidence, aimless future, work, and financial. The present study analyzed the factor structure of the long and short forms of the WDQ (WDQ and WDQ-SF, respectively) through confirmatory factor analysis in a sample of 262 students (M age = 21.8; SD = 2.6; 86.3% females). While the goodness-of-fit indices did not provide support for the WDQ, good fit indices were found for the WDQ-SF. Furthermore, no source of misspecification was identified, thus, supporting the factorial validity of the WDQ-SF scale. Significant positive correlations between the WDQ-SF and its subscales with worry (PSWQ), anxiety (STAI-T), and depression (BDI) were found. The internal consistency was good for the total scale and for the subscales. This work provides support for the use of the WDQ-SF, and potential uses for research and clinical purposes are discussed.

Finding Goodness of Fit When You are Black, Poor, Male, and Disturbed

1988 ◽  
Vol 33 (10) ◽  
pp. 885-886
Author(s):  
Judith K. Grosenick
Keyword(s):  
Goodness Of Fit ◽  
Black Poor
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