Probabilistic Modeling of Monthly Temperature Historical Series in Mossoró, Northeastern Brazil

Objetivou-se verificar o ajuste de 12 séries históricas de pressão atmosférica mensal (milibar) no período de 1970 a2007, em Mossoró, RN, à sete modelos de distribuição densidade de probabilidade Normal, Log-Normal, Beta, Gama, Log-Pearson (Tipo III), Gumbel e Weibull, através dos testes Kolmogorov-Smirnov, Qui-Quadrado, Cramer Von-Mises, Anderson Darling e Kuiper a 10 % de probabilidade e utilizando-se o Logaritmo da Máxima Verossimilhança. Verificou-se a superioridade do ajustamento da distribuição de probabilidade Normal, quando comparada com as outras seis distribuições. No geral, os critérios de ajuste concordaram com a aceitação da hipótese H0, no entanto, deve-se salientar que o teste de Kolmogorov-Smirnov apresenta um nível de aprovação de uma distribuição sob teste muito elevado, gerando insegurança aos critérios do teste, porém, como neste estudo os dados são aproximadamente simétricos, esse é o mais recomendado.Probability distributions for historic series of monthly atmospheric pressure in city of Mossoró-RNAbstract: The aim of this study was to determine the set of 12 time series of monthly atmospheric pressure (millibars) in the period 1970-2007, in Natal, RN, the seven models of the probability density distribution Normal, Log-Normal, Beta, Gamma, Log -Pearson (Type III), Gumbel and Weibull, through the Kolmogorov-Smirnov tests, Chi-Square, Cramer-von Mises, Anderson Darling and Kuiper 10 probability and using the logarithm of the maximum likelihood. It is the superiority of adjusting the normal probability distribution compared to the other six distributions. Overall, the fit criteria agreed with the acceptance of the hypothesis, however, it should be noted that the Kolmogorov-Smirnov test shows a level of approval of a distribution under test very high, which creates some uncertainty to the criteria of test, but in this study as the data are roughly symmetrical it is the most recommended.

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

Astin Bulletin ◽

10.1017/s0515036100013519 ◽

2003 ◽

Vol 33 (2) ◽

pp. 365-381 ◽

Cited By ~ 19

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.

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On Markov Earth Mover's Distance

International Journal of Image and Graphics ◽

10.1142/s0219467814500168 ◽

2014 ◽

Vol 14 (04) ◽

pp. 1450016 ◽

Cited By ~ 1

Author(s):

Jie Wei

Keyword(s):

Goodness Of Fit ◽

Empirical Studies ◽

Earth Mover’S Distance ◽

Long Distance ◽

Chi Square ◽

Earth Mover's Distance ◽

The Earth ◽

Order Of Magnitude ◽

Kolmogorov Smirnov ◽

System Nodes

In statistics, pattern recognition and signal processing, it is of utmost importance to have an effective and efficient distance to measure the similarity between two distributions and sequences. In statistics this is referred to as goodness-of-fit problem. Two leading goodness of fit methods are chi-square and Kolmogorov–Smirnov distances. The strictly localized nature of these two measures hinders their practical utilities in patterns and signals where the sample size is usually small. In view of this problem Rubner and colleagues developed the earth mover's distance (EMD) to allow for cross-bin moves in evaluating the distance between two patterns, which find a broad spectrum of applications. EMD-L1 was later proposed to reduce the time complexity of EMD from super-cubic by one order of magnitude by exploiting the special L1 metric. EMD-hat was developed to turn the global EMD to a localized one by discarding long-distance earth movements. In this work, we introduce a Markov EMD (MEMD) by treating the source and destination nodes absolutely symmetrically. In MEMD, like hat-EMD, the earth is only moved locally as dictated by the degree d of neighborhood system. Nodes that cannot be matched locally is handled by dummy source and destination nodes. By use of this localized network structure, a greedy algorithm that is linear to the degree d and number of nodes is then developed to evaluate the MEMD. Empirical studies on the use of MEMD on deterministic and statistical synthetic sequences and SIFT-based image retrieval suggested encouraging performances.

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.806.173 ◽

2015 ◽

Vol 806 ◽

pp. 173-180 ◽

Cited By ~ 1

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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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 of Reference Evapotranspiration to Gamma Probability Distribution

Journal of Agricultural Science ◽

10.5539/jas.v13n6p70 ◽

2021 ◽

Vol 13 (6) ◽

pp. 70

Author(s):

Janilson Pinheiro de Assis ◽

Roberto Pequeno de Sousa ◽

Isaac Reinaldo Pinheiro de Lima ◽

Paulo César Ferreira Linhares ◽

Walter Rodrigues Martins ◽

...

Keyword(s):

Probability Distribution ◽

Gamma Distribution ◽

Goodness Of Fit ◽

Reference Evapotranspiration ◽

Chi Square ◽

Confidence Levels ◽

Use Of Data ◽

Maximum Benefit ◽

Kolmogorov Smirnov ◽

Data Period

This paper aims to estimate, using the Penman-Monteith method, the probabilities of reference evapotranspiration (ET0) in millimeters, as well as their accumulated values for ten days (decendial), in Mossoró, northeast Brazil. The Meteorological Station of the Federal Rural University of Semi-Arid (UFERSA) provided the daily records of evapotranspiration. The construction of tables based on the approximation of the variable to the Gamma distribution allows the use of data without transformations. The probabilities were estimated with the Gamma distribution at confidence levels of 1% to 95% over the 1970-2007 data period. The results of the chi-square and Kolmogorov-Smirnov tests at 10% probability (p ≥ 0.10) demonstrated the adequacy of the table construction process, providing essential support in the planning of agricultural activities in the region to obtain the maximum benefit from evapotranspiration data. The Gamma probability distribution best described the ET0 for scaling irrigation systems in the county. The maximum daily ET0 for irrigation projects in the Mossoró region is 10 mm, and the cumulative 10-day ET0 averages 80 mm.

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TESTING INDEPENDENCE IN TIME SERIES VIA UNIVERSAL DISTRIBUTIONS OF PERMUTATIONS AND WORDS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127405012788 ◽

2005 ◽

Vol 15 (05) ◽

pp. 1757-1765 ◽

Cited By ~ 3

Author(s):

CAMILLO CAMMAROTA ◽

ENRICO ROGORA

Keyword(s):

Time Series ◽

General Framework ◽

Goodness Of Fit ◽

Probability Distributions ◽

Recursive Algorithm ◽

Chi Square ◽

Independent Sequence ◽

Empirical Distributions ◽

Testing Independence ◽

Analysis Of Time Series

We study probability distributions of permutations and binary words, which arise in symbolic analysis of time series and their differences. Under the assumptions that the series is stationary and independent we show that these probability distributions are universal and we derive a recursive algorithm for computing the distribution of binary words. This provides a general framework for performing chi square tests of goodness of fit of empirical distributions versus universal ones. We apply these methods to analyze heartbeat time series; in particular, we measure the extent to which atrial fibrillation can be modeled as an independent sequence.

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

Astin Bulletin ◽

10.2143/ast.33.2.503698 ◽

2003 ◽

Vol 33 (02) ◽

pp. 365-381 ◽

Cited By ~ 16

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.

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Climate Change Impacts on Rainfall Distribution at Teluk Intan Catchment

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.773-774.1296 ◽

2015 ◽

Vol 773-774 ◽

pp. 1296-1300 ◽

Cited By ~ 2

Author(s):

Zawani Mohd Zahudi ◽

Mohd Shalahuddin Adnan ◽

Nurul Farehah Amat ◽

Yuliarahmadila Erfen ◽

Noorfathiah Che Ali

Keyword(s):

Climate Change ◽

Goodness Of Fit ◽

Sea Water ◽

Rainfall Pattern ◽

Total Rainfall ◽

Rainfall Distribution ◽

Chi Square ◽

Drought Period ◽

Pearson Type ◽

Chi Square Test

Many studies have been conducted on determining the effect of climate change on the precipitation. The increasing of temperature has led to increase of evaporation rate, rainfall intensity, sea water level and so forth. These changes will lead to greater disaster such as increase of flood magnitude, flood event, drought intensity and prolong the drought period. The main objective of this study is to analyze the monthly rainfall pattern from 1984 to 1993 for the Teluk Intan Basin. Five stations of rainfall data were retrieved from DID. The rainfall distribution pattern was calculated by using two types of probability distributions known as Log-Pearson type-III and Gumbel using California’s method. Later, Chi-square test of goodness of fit was applied to validate the results. Based on the calculated results, out of the five stations used in this study, only three stations shows are fitted to apply the mentioned method which is Mengkuang River St, Labu Kubong St and Telok Intan station. Maximum total rainfall for ten years period occurs at Pt. IV Sg. Manik St as the value is 5570.5 mm, meanwhile minimum total rainfall occurs at Pt. I Sg. Manik St as the value is 1462.5 mm. For the average temperature, year 1990 gives the maximum value that is 29.18°C, while year 1986 gives the minimum value that is 28.79°C. The chi-square test was performed to determine which method is fitted to use as statistical analyses. Lastly, correlation test was tested to determine the correlation between rainfall and temperature. Based on the correlation result, it clearly shows a weak correlation between rainfall and temperature. For Telok Intan St the correlation value is 0.17, Pt. I Sg. Manik St is 0.28, Mengkuang River St is 0.17, Pt. IV Sg. Manik St is 0.4, and lastly Labu Kubong St gives the smallest correlation value that is 0.07. As a conclusion, the distributions of rainfall pattern in this area are not really affected by the temperature. However, the temperature distribution still will affect the rainfall distribution in a longer period.

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