scholarly journals A Density-Based Empirical Likelihood Ratio Approach for Goodness-of-fit Tests in Decreasing Densities

2020 ◽  
Vol 8 (1) ◽  
pp. 66-79
Author(s):  
Vahid Fakoor ◽  
Masoud Ajami ◽  
Seyed Mahdi Amir Jahanshahi ◽  
Ali Shariati
Keyword(s):  
Empirical Likelihood ◽  
Null Hypothesis ◽  
Goodness Of Fit ◽  
Real Data ◽  
Distribution Functions ◽  
Test Statistic ◽  
Goodness Of Fit Tests ◽  
Alternative Hypotheses ◽  
Ratio Approach ◽  
Consistency Of The Test

In this paper, we propose a test for the null hypothesis that a decreasing density function belongs to a givenparametric family of distribution functions against the non-parametric alternative. This method, which is based on an empirical likelihood (EL) ratio statistic, is similar to the test introduced by Vexler and Gurevich [23]. The consistency of the test statistic proposed is derived under the null and alternative hypotheses. A simulation study is conducted to inspect the power of the proposed test under various decreasing alternatives. In each scenario, the critical region of the test is obtained using a Monte Carlo technique. The applicability of the proposed test in practice is demonstrated through a few real data examples.  

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.

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.

Temporal and spatial variations in annual rainfall distribution in Erbil province

2018 ◽  
Vol 47 (1) ◽  
pp. 59-67
Author(s):  
Tariq H Karim ◽  
Dawod R Keya ◽  
Zahir A Amin
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Kendall Test ◽  
Distribution Functions ◽  
Annual Rainfall ◽  
Maximum Rainfall ◽  
Probability Distribution Functions ◽  
Goodness Of Fit Tests ◽  
Annual Maximum Rainfall ◽  
Best Fit

This study aimed to determine the best fit probability distribution of annual maximum rainfall using data from nine stations within Erbil province using different statistical analyses. Nine commonly used probability distribution functions, namely Normal, Lognormal (LN), one-parameter gamma (1P-G), 2P-G, 3P-G, Log Pearson, Weibull, Pareto, and Beta, were assessed. On the basis of maximum overall score, obtained by adding individual point scores from three selected goodness-of-fit tests, the best fit probability distribution was identified. Results showed that the 2P-G distribution and LN distribution were the best fit probability distribution functions for annual rainfall for the region. The analysis of annual rainfall records in Erbil city spanning from 1964 to 2013, covering three periods, also revealed significant temporal changes in the shape and scale parameter patterns of the fitted gamma distribution. Based on the reliable annual rainfall data in the region, the shape and scale parameters were then regionalized, hence it is possible to find the parameter values for any desired location within the study area. The Mann–Kendall test results indicated that there was a decreasing trend in rainfall over most of the study area in recent decades.

scholarly journals Odd Lomax-Kumaraswamy Distribution: Its Properties and Applications

2020 ◽  
pp. 45-60
Author(s):  
Bassa Shiwaye Yakura ◽  
Ahmed Askira Sule ◽  
Mustapha Mohammed Dewu ◽  
Kabiru Ahmed Manju ◽  
Fadimatu Bawuro Mohammed
Keyword(s):  
Goodness Of Fit ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Distribution Functions ◽  
Model Parameters ◽  
Data Sets ◽  
Kumaraswamy Distribution ◽  
Method Of Maximum Likelihood ◽  
Family Of Distributions

This article uses the odd Lomax-G family of distributions to study a new extension of the Kumaraswamy distribution called “odd Lomax-Kumaraswamy distribution”. In this article, the density and distribution functions of the odd Lomax-Kumaraswamy distribution are defined and studied with many other properties of the distribution such as the ordinary moments, moment generating function, characteristic function, quantile function, reliability functions, order statistics and other useful measures. The model parameters are estimated by the method of maximum likelihood. The goodness-of-fit of the proposed distribution is demonstrated using two real data sets.

scholarly journals Goodness of Fit Tests for Marshal-Olkin Extended Rayleigh Distribution

2019 ◽  
pp. 587-598
Author(s):  
Naz Saud ◽  
Sohail Chand
Keyword(s):  
Goodness Of Fit ◽  
Empirical Distribution ◽  
Rayleigh Distribution ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Goodness Of Fit Tests ◽  
Estimated Parameters ◽  
Percentage Points ◽  
Anderson Darling ◽  
Von Mises

A class of goodness of fit tests for Marshal-Olkin Extended Rayleigh distribution with estimated parameters is proposed. The tests are based on the empirical distribution function. For determination of asymptotic percentage points, Kolomogorov-Sminrov, Cramer-von-Mises, Anderson-Darling,Watson, and Liao-Shimokawa test statistic are used. This article uses Monte Carlo simulations to obtain asymptotic percentage points for Marshal-Olkin extended Rayleigh distribution. Moreover, power of the goodness of fit test statistics is investigated for this lifetime model against several alternatives.

Stochastic model of contractions at a point in the duodenum

1975 ◽  
Vol 229 (3) ◽  
pp. 613-617 ◽  
Author(s):  
RB Singerman ◽  
EO Macagno ◽  
Glover ◽  
J Christensen
Keyword(s):  
Slow Wave ◽  
Goodness Of Fit ◽  
Human Subjects ◽  
Real Data ◽  
Type Model ◽  
Chi Square ◽  
Frequency Distributions ◽  
The Real ◽  
Goodness Of Fit Tests ◽  
Wave Cycle

Contractions at one point in the human duodenum were studied as a time series. Manometric records were made over long time periods from the duodenum in fed human subjects. A 5-s grid was superimposed on the time axis of the records. Each 5-s interval was treated as a slow-wave cycle within which either a contraction or a no-contraction could occur. The resulting series of alternating runs of contractions and no-contractions was tested for the existence of trends. Trends were found indicating possible temporal dependence. A Markov-type model was used to try to generate data similar to the real data. Success was achieved by a model that assumed a probability of contraction dependent on the three previous slow-wave cycles. The frequency distributions obtained from the real and generated data were compared using Chi-square goodness-of-fit tests and found to be statistically similar. The correlations in time found for the contractions might be due to a time dependency in the controls for contraction over four successive slow-wave periods, 20 s in humans.

Robust bi-level risk-based optimal scheduling of microgrid operation against uncertainty

2020 ◽  
Vol 54 (4) ◽  
pp. 993-1012 ◽  
Author(s):  
Hêriș Golpîra ◽  
Salah Bahramara ◽  
Syed Abdul Rehman Khan ◽  
Yu Zhang
Keyword(s):  
Risk Aversion ◽  
Value At Risk ◽  
Goodness Of Fit ◽  
Distribution Functions ◽  
Optimal Scheduling ◽  
Conditional Value At Risk ◽  
Optimization Approach ◽  
Goodness Of Fit Tests ◽  
The Cost ◽  
Initial Objective

The model introduced in this paper is the first to propose a decentralized robust optimal scheduling of MG operation under uncertainty and risk. The power trading of the MG with the main grid is the first stage variable and power generation of DGs and power charging/discharging of the battery are the second stage variables. The uncertain term of the initial objective function is transformed into a constraint using robust optimization approach. Addressing the Decision Maker’s (DMs) risk aversion level through Conditional Value at Risk (CVaR) leads to a bi-level programming problem using a data-driven approach. The model is then transformed into a robust single-level using Karush–Kahn–Tucker (KKT) conditions. To investigate the effectiveness of the model and its solution methodology, it is applied on a MG. The results clearly demonstrate the robustness of the model and indicate a strong almost linear relationship between cost and the DMs various levels of risk aversion. The analysis also outlines original characterization of the cost and the MGs behavior using three well-known goodness-of-fit tests on various Probability Distribution Functions (PDFs), Beta, Gumbel Max, Normal, Weibull, and Cauchy. The Gumbel Max and Normal PDFs, respectively, exhibit the most promising goodness-of-fit for the cost, while the power purchased from the grid are well fitted by Weibull, Beta, and Normal PDFs, respectively. At the same time, the power sold to the grid is well fitted by the Cauchy PDF.

scholarly journals A generalized Anderson–Darling test for the goodness-of-fit evaluation of the fracture strain distribution of acrylic glass

2021 ◽  
Author(s):  
Marcel Berlinger ◽  
Stefan Kolling ◽  
Jens Schneider
Keyword(s):  
Goodness Of Fit ◽  
Tensile Tests ◽  
Distribution Functions ◽  
Image Correlation ◽  
Strain Behavior ◽  
Probability Estimator ◽  
Goodness Of Fit Tests ◽  
Static Tensile ◽  
Structural Parts ◽  
Anderson Darling

AbstractAcrylic glasses, as well as mineral glasses, exhibit a high variability in tensile strength. To cope with this uncertainty factor for the dimensioning of structural parts, modeling of the stress-strain behavior and a proper characterization of the varying fracture stress or strain are required. For the latter, this work presents an experimental and mathematical methodology. Fracture strains from 50 quasi-static tensile tests, locally analyzed using digital image correlation, form the sample. For the assignment of an occurrence probability to each experiment, an evaluation of existing probability estimators is conducted, concerning their ability to fit selected probability distribution functions. Important goodness-of-fit tests are introduced and assessed critically. Based on the popular Anderson-Darling test, a generalized form is proposed that allows a free, hitherto not possible, choice of the probability estimator. To approach the fracture strains population, the combination of probability estimator and distribution function that best reproduces the experimental data is determined, and its characteristic progression is discussed with the aid of fractographic analyses.

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