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 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 Goodness of fit tests for Rayleigh distribution based on Phi-divergence

2017 ◽  
Vol 40 (2) ◽  
pp. 279-290 ◽  
Author(s):  
Mahdi Mahdizadeh ◽  
Ehsan Zamanzade
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Goodness Of Fit ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Data Set ◽  
Goodness Of Fit Tests ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Von Mises

In this paper, we develop some goodness of fit tests for Rayleigh distribution based on Phi-divergence. Using Monte Carlo simulation, we compare the power of the proposed tests with some traditional goodness of fit tests including Kolmogorov-Smirnov, Anderson-Darling and Cramer von-Mises tests. The results indicate that the proposed tests perform well as compared with their competing tests in the literature. Finally, the proposed procedures are illustrated via a real data set.

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 Performances of Shannon’s Entropy Statistic in Assessment of Distribution of Data

2017 ◽  
Vol 28 (2) ◽  
pp. 30-42 ◽  
Author(s):  
Lorentz Jäntschi ◽  
Sorana D. Bolboacă
Keyword(s):  
Experimental Data ◽  
Goodness Of Fit ◽  
Error Function ◽  
Shannon’S Entropy ◽  
Goodness Of Fit Test ◽  
Shannon's Entropy ◽  
Goodness Of Fit Tests ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Von Mises

AbstractStatistical analysis starts with the assessment of the distribution of experimental data. Different statistics are used to test the null hypothesis (H0) stated as Data follow a certain/specified distribution. In this paper, a new test based on Shannon’s entropy (called Shannon’s entropy statistic, H1) is introduced as goodness-of-fit test. The performance of the Shannon’s entropy statistic was tested on simulated and/or experimental data with uniform and respectively four continuous distributions (as error function, generalized extreme value, lognormal, and normal). The experimental data used in the assessment were properties or activities of active chemical compounds. Five known goodness-of-fit tests namely Anderson-Darling, Kolmogorov-Smirnov, Cramér-von Mises, Kuiper V, and Watson U2 were used to accompany and assess the performances of H1.

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.

Fitting The Statistical Distributions To The Daily Rainfall Amount In Peninsular Malaysia

2012 ◽  
Author(s):  
Suhaila Jamaludin ◽  
Abdul Aziz Jemain
Keyword(s):  
Goodness Of Fit ◽  
Daily Rainfall ◽  
Peninsular Malaysia ◽  
Rainfall Amount ◽  
Likelihood Method ◽  
Goodness Of Fit Test ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Von Mises ◽  
Cramer Von Mises

Data hujan harian dibahagikan kepada empat jenis rentetan hujan (jenis 1, 2, 3 dan 4). Taburan Gamma, Weibull, Kappa dan Gabungan Eksponen ialah empat taburan statistik yang diuji dalam memadankan data jumlah hujan harian di Semenanjung Malaysia. Parameter bagi setiap taburan dianggar dengan menggunakan kaedah kebolehjadian maksimum. Model dipilih berdasarkan nilai ralat yang minimum terhasil dari tujuh ujian kesesuaian model iaitu median bagi perbezaan nilai mutlak antara taburan empirik dengan taburan yang diuji, statistik fungsi empirik iaitu Kolmogorov-Smirnov D, Anderson Darling A2 dan Cramer-von-Mises W2 serta kaedah baru statistik fungsi empirik yang berasaskan kepada ujian nisbah kebolehjadian. Berdasarkan nilai ujian kesesuaian model, didapati taburan Gabungan Eksponen adalah yang paling sesuai dalam memadankan data jumlah hujan harian di Semenanjung Malaysia. Kata kunci: Jumlah hujan harian, ujian kesesuaian model, gabungan eksponen Daily rainfall data have been classified according to four rain types of sequence of wet days (Type 1, 2, 3 and 4). The Gamma, Weibull, Kappa and Mixed Exponential are the four distributions that have been tested to fit daily rainfall amount in Peninsular Malaysia. Parameter for each distribution were estimated using the maximum likelihood method. The selected model is chosen based on the minimum error produced by seven goodness-of-fit (GOF) tests namely the medium of absolute difference (MAD) between the empirical and hypothesized distributions, the traditional Empirical Distribution Function (EDF) Statistics which include Kolmogorov-Smirnov statistic D, Anderson Darling statistic A2 and Cramer-von-Mises statistic W2 and the new method of EDF Statistic based on likelihood ratio statistic. Based on these goodness-of-fit test, the Mixed Exponential is found to be the most approriate distribution for describing the daily rainfall amount in Peninsular Malaysia. Key words: Dairy rainfall amount, goodness–of–fit test, mixed exponential

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 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.

Reliability Analysis of the Hydro-System of Excavator SchRs 800 Using Weibull Distribution

2015 ◽  
Vol 806 ◽  
pp. 173-180 ◽  
Author(s):  
Predrag Dašić ◽  
Milutin Živković ◽  
Marina Karić
Keyword(s):  
Weibull Distribution ◽  
Reliability Analysis ◽  
Goodness Of Fit ◽  
Weibull Model ◽  
Reliability Model ◽  
Goodness Of Fit Tests ◽  
Kolmogorov Smirnov ◽  
Von Mises

In this paper is given the use Weibull distribution (WD) as theoretical reliability model for analysis of the hydro-system of excavator SchRs 800, which is accepted on the basis of Pearson (χ2), Kolmogorov-Smirnov (KS) and Cramér-von Mises (CvM) goodness-of-fit tests. The time of work without failure of the hydro-system of excavator SchRs 800 for accepted Weibull model of reliability for probability of 50 % is T50%=0.3417⋅103[h], for probability of 80 % is T80%=0.1884⋅103[h] and for probability of 90% is T90%=0.127⋅103[h].

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