Favorable Estimators for Fitting Pareto Models: A Study Using Goodness-of-fit Measures with Actual Data

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.

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Goodness-of-fit tests for the beta Gompertz distribution

Thermal Science ◽

10.2298/tsci20069a ◽

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.

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Goodness-of-fit tests for the beta Gompertz distribution

Thermal Science ◽

10.2298/tsci20s1069a ◽

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.

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

Revista Colombiana de Estadística ◽

10.15446/rce.v40n2.60375 ◽

2017 ◽

Vol 40 (2) ◽

pp. 279-290 ◽

Cited By ~ 3

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.

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

Ovidius University Annals of Chemistry ◽

10.1515/auoc-2017-0006 ◽

2017 ◽

Vol 28 (2) ◽

pp. 30-42 ◽

Cited By ~ 8

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.

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

Jurnal Teknologi ◽

10.11113/jt.v46.287 ◽

2012 ◽

Cited By ~ 2

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

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The transmuted generalized modified Weibull distribution

Filomat ◽

10.2298/fil1705395c ◽

2017 ◽

Vol 31 (5) ◽

pp. 1395-1412 ◽

Cited By ~ 2

Author(s):

Gaussm Cordeiro ◽

Abdus Saboor ◽

Muhammad Khan ◽

Serge Provost

Keyword(s):

Weibull Distribution ◽

Goodness Of Fit ◽

Real Data ◽

Rate Function ◽

Modified Weibull Distribution ◽

Positive Data ◽

Anderson Darling ◽

Generalized Modified Weibull ◽

Modified Weibull ◽

Von Mises

Canada EM [email protected] AU Ortega Edwinm M. AF Universidade de S?o Paulo, Departamento de Ci?ncias Exatas, Piracicaba, Brazil EM [email protected] KW Generalized modifiedWeibull distribution % Goodness-of-fit statistic % Lifetime data % Transmuted family % Weibull distribution KR nema A profusion of new classes of distributions has recently proven useful to applied statisticians working in various areas of scientific investigation. Generalizing existing distributions by adding shape parameters leads to more flexible models. We define a new lifetime model called the transmuted generalized modified Weibull distribution from the family proposed by Aryal and Tsokos [1], which has a bathtub shaped hazard rate function. Some structural properties of the new model are investigated. The parameters of this distribution are estimated using the maximum likelihood approach. The proposed model turns out to be quite flexible for analyzing positive data. In fact, it can provide better fits than related distributions as measured by the Anderson-Darling (A*) and Cram?r-von Mises (W*) statistics, which is illustrated by applying it to two real data sets. It may serve as a viable alternative to other distributions for modeling positive data arising in several fields of science such as hydrology, biostatistics, meteorology and engineering.

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Applying the Anderson-Darling Test to Suicide Clusters

Crisis ◽

10.1027/0227-5910/a000197 ◽

2013 ◽

Vol 34 (6) ◽

pp. 434-437 ◽

Cited By ~ 5

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.

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Bootstrap Analysis

10.1093/oso/9780198505044.003.0004 ◽

2017 ◽

Author(s):

Russell Cheng

Keyword(s):

Goodness Of Fit ◽

Null Distribution ◽

Real Data ◽

Confidence Regions ◽

Confidence Bands ◽

Cumulative Distribution ◽

Attractive Alternative ◽

Bootstrap Analysis ◽

Parametric Bootstrapping ◽

Anderson Darling

Parametric bootstrapping (BS) provides an attractive alternative, both theoretically and numerically, to asymptotic theory for estimating sampling distributions. This chapter summarizes its use not only for calculating confidence intervals for estimated parameters and functions of parameters, but also to obtain log-likelihood-based confidence regions from which confidence bands for cumulative distribution and regression functions can be obtained. All such BS calculations are very easy to implement. Details are also given for calculating critical values of EDF statistics used in goodness-of-fit (GoF) tests, such as the Anderson-Darling A2 statistic whose null distribution is otherwise difficult to obtain, as it varies with different null hypotheses. A simple proof is given showing that the parametric BS is probabilistically exact for location-scale models. A formal regression lack-of-fit test employing parametric BS is given that can be used even when the regression data has no replications. Two real data examples are given.

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Aplicação da Distribuição Nakagami na Análise de Dados de Precipitação

Revista Brasileira de Meteorologia ◽

10.1590/0102-77863340011 ◽

2019 ◽

Vol 34 (1) ◽

pp. 1-7

Author(s):

Josmar Mazucheli ◽

Isabele Picada Emanuelli

Keyword(s):

Kolmogorov Smirnov ◽

Anderson Darling ◽

Log Normal ◽

Von Mises ◽

Cramer Von Mises

Resumo Este trabalho teve como objetivo avaliar o desempenho da distribuição Nakagami na análise de séries de precipitação mensal, ao longo de vários anos, visando à seleção de uma distribuição útil para o planejamento e gestão de atividades dependentes dos índices de precipitação na Região Sul do Brasil. Para tanto, compara-se a mesma com cinco distribuições alternativas: Weibull, Gama, Log-Normal, Log-Logística e Inversa-Gaussiana. Foram utilizadas séries históricas de 33 estações meteorológicas observadas entre janeiro de 1970 a dezembro de 2014, totalizando 396 séries (33 estações × 12 meses). Para a escolha da distribuição, que forneceu o melhor ajuste, foram utilizados os valores dos critérios de informação de Akaike, de Kolmogorov-Smirnov, de Anderson-Darling e de Cramér-von Mises. Segundo estes critérios se encontrou que as distribuições Nakagami e Weibull foram selecionadas o maior número de vezes (Nakagami: 146 vezes e Weibull: 100 vezes). Embora a distribuição Nakagami não seja muito utilizada, na descrição de dados de precipitação, recomenda-se sua utilização na descrição do comportamento da pluviosidade mensal como alternativa para distribuições tradicionalmente utilizadas.

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