A test for fuzzy exponentiality based on Kullback-Leibler information

2021 ◽  
pp. 1-8
Author(s):  
Lingtao Kong
Keyword(s):  
Biological Sciences ◽  
Monte Carlo ◽  
Goodness Of Fit ◽  
Experimental Studies ◽  
Real Data ◽  
Test Statistics ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Higher Power ◽  
Leibler Information

The exponential distribution has been widely used in engineering, social and biological sciences. In this paper, we propose a new goodness-of-fit test for fuzzy exponentiality using α-pessimistic value. The test statistics is established based on Kullback-Leibler information. By using Monte Carlo method, we obtain the empirical critical points of the test statistic at four different significant levels. To evaluate the performance of the proposed test, we compare it with four commonly used tests through some simulations. Experimental studies show that the proposed test has higher power than other tests in most cases. In particular, for the uniform and linear failure rate alternatives, our method has the best performance. A real data example is investigated to show the application of our test.

scholarly journals ON APPROXIMATING THE DISTRIBUTIONS OF GOODNESS-OF-FIT TEST STATISTICS BASED ON THE EMPIRICAL DISTRIBUTION FUNCTION: THE CASE OF UNKNOWN PARAMETERS

2009 ◽  
Vol 12 (02) ◽  
pp. 157-167 ◽  
Author(s):  
MARCO CAPASSO ◽  
LUCIA ALESSI ◽  
MATTEO BARIGOZZI ◽  
GIORGIO FAGIOLO
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Goodness Of Fit ◽  
Empirical Distribution Function ◽  
Empirical Distribution ◽  
Test Statistics ◽  
Test Statistic ◽  
Unknown Parameters ◽  
Goodness Of Fit Test ◽  
The Impact

This paper discusses some problems possibly arising when approximating via Monte-Carlo simulations the distributions of goodness-of-fit test statistics based on the empirical distribution function. We argue that failing to re-estimate unknown parameters on each simulated Monte-Carlo sample — and thus avoiding to employ this information to build the test statistic — may lead to wrong, overly-conservative. Furthermore, we present some simple examples suggesting that the impact of this possible mistake may turn out to be dramatic and does not vanish as the sample size increases.

scholarly journals A powerful goodness-of-fit test for Lindley distribution with application to real data

2021 ◽  
pp. 761-769
Author(s):  
Hadi Alizadeh Noughabi
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Critical Points ◽  
Goodness Of Fit ◽  
Real Data ◽  
Reliability Model ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Lindley Distribution

The Lindley distribution may serve as a useful reliability model. Applications of this distribution are presented in statistical literature. In this article, a powerful goodness of fit test for the Lindley distribution is proposed. In order to compute the proposed test statistic, we use the maximum likelihood estimate (MLE) suggested by Ghitany et al. (2008), which is simple explicit estimator. By Monte Carlo simulation, critical points of the proposed test statistic for different sample sizes are obtained. Power values of the proposed test are compared with the competing tests against various alternatives via simulations. Finally, two real data are presented and analyzed.

ENTROPY-BASED AND NON-ENTROPY-BASED GOODNESS OF FIT TEST FOR THE INVERSE RAYLEIGH DISTRIBUTION WITH PROGRESSIVELY TYPE-II CENSORED DATA

2020 ◽  
pp. 1-19
Author(s):  
Yanbin Ma ◽  
Wenhao Gui
Keyword(s):  
Goodness Of Fit ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Type Ii ◽  
Test Statistics ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Data Set ◽  
Censored Samples ◽  
Type Ii Censored Data

In this paper, the problem of goodness of fit test for the inverse Rayleigh distribution based on progressively Type-II censored samples is studied. We develop two test statistics via entropy and propose one new non-entropy test statistic via a pivotal method. We also study the properties of these test statistics. Critical values are obtained by simulations. Then, we do power analysis of these test statistics against various alternatives under different censoring schemes. We conclude that the tests we proposed perform well against various alternatives, especially for non-monotone hazard alternatives. Finally, one real data set is analyzed.

scholarly journals Goodness-of-Fit Tests for Bivariate Time Series of Counts

Econometrics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 10
Author(s):  
Šárka Hudecová ◽  
Marie Hušková ◽  
Simos G. Meintanis
Keyword(s):  
Goodness Of Fit ◽  
Probability Generating Function ◽  
Parametric Bootstrap ◽  
Real Data ◽  
Data Sets ◽  
Test Statistics ◽  
Finite Sample ◽  
Generalized Poisson ◽  
Goodness Of Fit Tests ◽  
Monte Carlo Experiments

This article considers goodness-of-fit tests for bivariate INAR and bivariate Poisson autoregression models. The test statistics are based on an L2-type distance between two estimators of the probability generating function of the observations: one being entirely nonparametric and the second one being semiparametric computed under the corresponding null hypothesis. The asymptotic distribution of the proposed tests statistics both under the null hypotheses as well as under alternatives is derived and consistency is proved. The case of testing bivariate generalized Poisson autoregression and extension of the methods to dimension higher than two are also discussed. The finite-sample performance of a parametric bootstrap version of the tests is illustrated via a series of Monte Carlo experiments. The article concludes with applications on real data sets and discussion.

scholarly journals Testing in Nonparametric Accelerated Life Time Models

2016 ◽  
Vol 37 (1) ◽  
Author(s):  
Hannelore Liero
Keyword(s):  
Limit Distribution ◽  
Goodness Of Fit ◽  
Bootstrap Method ◽  
Life Time ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Time Model ◽  
Power Of The Test ◽  
Accelerated Life ◽  
Type Test

A goodness-of-fit test for testing the acceleration function in a nonparametric life time model is proposed. For this aim the limit distribution of an L2-type test statistic is derived. Furthermore, a bootstrap method is considered and the power of the test is studied.

scholarly journals Tracking Pandemic Severity Using Data on the Age Structure of Mortality: Lessons From the 1918 Influenza Pandemic in Michigan

2021 ◽  
Vol 111 (S2) ◽  
pp. S149-S155
Author(s):  
Siddharth Chandra ◽  
Julia Christensen
Keyword(s):  
Public Health ◽  
Age Structure ◽  
Goodness Of Fit ◽  
Influenza Pandemic ◽  
Age Distribution ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
1918 Influenza ◽  
Death Data ◽  
Excess Deaths

Objectives. To test whether distortions in the age structure of mortality during the 1918 influenza pandemic in Michigan tracked the severity of the pandemic. Methods. We calculated monthly excess deaths during the period of 1918 to 1920 by using monthly data on all-cause deaths for the period of 1912 to 1920 in Michigan. Next, we measured distortions in the age distribution of deaths by using the Kuiper goodness-of-fit test statistic comparing the monthly distribution of deaths by age in 1918 to 1920 with the baseline distribution for the corresponding month for 1912 to 1917. Results. Monthly distortions in the age distribution of deaths were correlated with excess deaths for the period of 1918 to 1920 in Michigan (r = 0.83; P < .001). Conclusions. Distortions in the age distribution of deaths tracked variations in the severity of the 1918 influenza pandemic. Public Health Implications. It may be possible to track the severity of pandemic activity with age-at-death data by identifying distortions in the age distribution of deaths. Public health authorities should explore the application of this approach to tracking the COVID-19 pandemic in the absence of complete data coverage or accurate cause-of-death data.

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