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 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.

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.

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 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 Characterization and Goodness-of-Fit Test of Pareto and Some Related Distributions Based on Near-Order Statistics

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Masoumeh Akbari
Keyword(s):  
Order Statistics ◽  
Goodness Of Fit ◽  
Pareto Distribution ◽  
Probability Function ◽  
Goodness Of Fit Test ◽  
Goodness Of Fit Tests ◽  
Kolmogorov Smirnov ◽  
Definition Of ◽  
Von Mises ◽  
First Moment

In this paper, a new definition of the number of observations near the kth order statistics is developed. Then some characterization results for Pareto and some related distributions are established in terms of mass probability function, first moment of these new counting random variables, and using completeness properties of the sequence of functions xn,0<x<1,n≥1. Finally, new goodness-of-fit tests based on these new characterizations for Pareto distribution are presented. And the power values of the proposed tests are compared with the power values of well-known tests such as Kolmogorov–Smirnov and Cramer-von Mises tests by Monte Carlo simulations.

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 Estimation of flood frequency using statistical method: Mahanadi River basin, India

2020 ◽  
Vol 3 (1) ◽  
pp. 189-207
Author(s):  
Sandeep Samantaray ◽  
Abinash Sahoo
Keyword(s):  
Stream Flow ◽  
Goodness Of Fit ◽  
Central India ◽  
Extreme Value ◽  
Flood Frequency ◽  
Goodness Of Fit Test ◽  
Mahanadi River ◽  
Goodness Of Fit Tests ◽  
Study Results ◽  
Anderson Darling

Abstract Estimating stream flow has a substantial financial influence, because this can be of assistance in water resources management and provides safety from scarcity of water and conceivable flood destruction. Four common statistical methods, namely, Normal, Gumbel max, Log-Pearson III (LP III), and Gen. extreme value method are employed for 10, 20, 30, 35, 40, 50, 60, 70, 75, 100, 150 years to forecast stream flow. Monthly flow data from four stations on Mahanadi River, in Eastern Central India, namely, Rampur, Sundargarh, Jondhra, and Basantpur, are used in the study. Results show that Gumbel max gives better flow discharge value than the Normal, LP III, and Gen. extreme value methods for all four gauge stations. Estimated flood values for Rampur, Sundargarh, Jondhra, and Basantpur stations are 372.361 m3/sec, 530.415 m3/sec, 2,133.888 m3/sec, and 3,836.22 m3/sec, respectively, considering Gumbel max. Goodness-of-fit tests for four statistical distribution techniques applied in the present study are also evaluated using Kolmogorov–Smirov, Anderson–Darling, Chi-squared tests at critical value 0.05 for the four proposed gauge stations. Goodness-of-fit test results show that Gen. extreme value gives best results at Rampur, Sundergarh, and Jondhra gauge stations followed by LP III, whereas LP III is the best fit for Basantpur, followed by Gen. extreme value.

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.

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].

scholarly journals Probability Distribution of Rainfall in Medan

2019 ◽  
Vol 1 (2) ◽  
pp. 43-49 ◽  
Author(s):  
Elly Rosmaini
Keyword(s):  
Probability Distribution ◽  
Gamma Distribution ◽  
Goodness Of Fit ◽  
Monthly Rainfall ◽  
Rainfall Data ◽  
Goodness Of Fit Test ◽  
Normal Distributions ◽  
Lognormal Distributions ◽  
Kolmogorov Smirnov ◽  
Anderson Darling

In this paper we chose three stations in Medan City , Indonesia to estimate Monthly Rainfall Data i.e. Tuntungan, Tanjung Selamat, and Medan Selayang Stations. We took the data from 2007 to 2016. In this case fitted with Normal, Gamma, and Lognormal Distributions. To estimate parameters, we used this method. Furthermore, Kolmogorov-Smirnov and Anderson Darling tests were used the goodness-of-fit test. The Gamma and Normal Distributions is suitable for Tuntungan and Medan Selayang Stations were stated by Kolmogorov-Smirnov's test. Anderson Darling's test stated that Gamma Distribution was suitable for all stations.

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