scholarly journals WIND SPEED ANALYSIS AT IKEJA, NIGERIA USING THE CONVENTIONAL PROBABILITY DENSITY FUNCTIONS

2018 ◽  
Vol 24 (3) ◽  
Author(s):  
OLUSEYI OGUNSOLA ◽  
OGUNSOLA OSAGIEDE
Keyword(s):  
Likelihood Estimation ◽  
Information Criteria ◽  
Distribution Functions ◽  
Parameter Estimates ◽  
Energy Potential ◽  
Chi Square ◽  
Chi Square Test ◽  
Anderson Darling ◽  
Von Mises ◽  
Best Fit

<p>The wind energy potential at Ikeja (Lat. 6.35 °N; Long. 3.20 °E), Nigeria was statistically analyzed using three of the mostly utilized conventional Probability Distribution Functions (PDFs) in order to determine which of these distributions would give the best means of analysis for wind in this particular location. The best fit test for these PDFs were determined from Akaike Information Criteria, Bayesian Information Criteria, Kolmogorov-Smirnov test, Cramer-von Mises statistics, Anderson-Darling Statistic, Mean Square Error and Chi-Square Test using Maximum Likelihood Estimation and Method of Moments as parameter estimates. The Weibull distribution gave the best fit in this location.</p>

scholarly journals WIND SPEED ANALYSIS AT IKEJA, NIGERIA USING THE CONVENTIONAL PROBABILITY DENSITY FUNCTIONS

2018 ◽  
Vol 24 (3) ◽  
pp. 20-32
Author(s):  
OLUSEYI OGUNSOLA ◽  
OFURE OSAGIEDE
Keyword(s):  
Likelihood Estimation ◽  
Information Criteria ◽  
Distribution Functions ◽  
Parameter Estimates ◽  
Energy Potential ◽  
Chi Square ◽  
Chi Square Test ◽  
Anderson Darling ◽  
Von Mises ◽  
Best Fit

The wind energy potential at Ikeja (Lat. 6.35 N; Long. 3.20 E), Nigeria was statistically analyzed using three of the mostly utilized conventional Probability Distribution Functions (PDFs) in order to determine which of these distributions would give the best means of analysis for wind in this particular location. The best fit test for these PDFs were determined from Akaike Information Criteria, Bayesian Information Criteria, Kolmogorov-Smirnov test, Cramer-von Mises statistics, Anderson-Darling Statistic, Mean Square Error and Chi-Square Test using Maximum Likelihood Estimation and Method of Moments as parameter estimates. The Weibull distribution gave the best fit in this location.

scholarly journals Frequency analysis of annual one day to five consecutive days maximum rainfall for Gandak river basin

2014 ◽  
Vol 3 (2) ◽  
pp. 93 ◽  
Author(s):  
Shivika Singla ◽  
Raktim Halder ◽  
Rakesh Khosa ◽  
Rumani Singla ◽  
Rudraksh Rajeev
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Frequency Estimation ◽  
Distribution Functions ◽  
Chi Square ◽  
Maximum Rainfall ◽  
Thiessen Polygon ◽  
Chi Square Test ◽  
Arc Gis ◽  
Best Fit

The present study has been conducted for rainfall intensity and frequency estimation for the Gandak basin, a region prone to high floods with an unrealized and unexplored hydro-potential. The two popular gridded precipitation datasets i.e.: (1) APHRODITE, and (2) IMD, for the years 1969-2005, has been used to calculate the mean basin precipitation through the Thiessen polygon method on the ARC-GIS interface. This computed data was used to find out the 1-day, 2-day to 5-day consecutive maximum precipitation series and hence fitted into various well-known probability distribution functions viz., Normal, Gamma, Exponential, etc. According to the best fit data in these functions, the quantiles were determined corresponding to a return period of 2, 10, 20, 25, 50 and 100 years. The two widely used tests: Chi-square Test and Kolmogorov-Smirnov Test were employed to further check the goodness of fit of the series in the distributions. The results reveal that the best fit for 1-day was achieved with the normal distribution, for 2-day with GEV and with GPAR for the remaining maximum consecutive days rainfall. Such studies have thus proven to be substantially facilitative in planning for the safe and economic design of various engineered structures such as bridges, culverts, levees, canals, irrigation and drainage works and effective reservoir management. Keywords: Floods, Frequency, Hydrology, Probability Distribution, Rainfall.

Prediction of Haemoglobin Level by Some Probability Distribution

2020 ◽  
Vol 9 (1) ◽  
pp. 84-88
Author(s):  
Govinda Prasad Dhungana ◽  
Laxmi Prasad Sapkota
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Goodness Of Fit ◽  
Continuous Variable ◽  
Hemoglobin Level ◽  
Chi Square ◽  
Chi Square Test ◽  
Log Normal ◽  
Two Parameters ◽  
Best Fit

 Hemoglobin level is a continuous variable. So, it follows some theoretical probability distribution Normal, Log-normal, Gamma and Weibull distribution having two parameters. There is low variation in observed and expected frequency of Normal distribution in bar diagram. Similarly, calculated value of chi-square test (goodness of fit) is observed which is lower in Normal distribution. Furthermore, plot of PDFof Normal distribution covers larger area of histogram than all of other distribution. Hence Normal distribution is the best fit to predict the hemoglobin level in future.

scholarly journals The Topp-Leone Weibull Distribution: Its Properties and Application

2021 ◽  
pp. 381-401
Author(s):  
Diamond O. Tuoyo ◽  
Festus C. Opone ◽  
N. Ekhosuehi
Keyword(s):  
Weibull Distribution ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Information Criterion ◽  
Lifetime Data ◽  
Test Statistic ◽  
Data Set ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Von Mises

This paper presents a new generalization of the Topp-Leone distribution called the Topp-Leone Weibull Distribution (TLWD). Some of the mathematical properties of the proposed distribution are derived, and the maximum likelihood estimation method is adopted in estimating the parameters of the proposed distribution. An application of the proposed distribution alongside with some well-known distributions belonging to the Topp-Leone generated family of distributions, to a real lifetime data set reveals that the proposed distribution exhibits more flexibility in modeling lifetime data based on some comparison criteria such as maximized log-likelihood, Akaike Information Criterion [AIC=2k-2 log⁡(L) ], Kolmogorov-Smirnov test statistic (K-S) and Anderson Darling test statistic (A*) and Crammer-Von Mises test statistic (W*).

scholarly journals Statistical Distribution of Rainfall in Kurdistan-Iraq Region

2020 ◽  
Vol 30 (4) ◽  
pp. 18
Author(s):  
Meeran Akram Fawzee ◽  
Samira M. Salh ◽  
Slahaddin A. Ahmed
Keyword(s):  
Goodness Of Fit ◽  
Extreme Value ◽  
Rainfall Amount ◽  
Statistical Distribution ◽  
Rainfall Series ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Anderson Darling ◽  
Best Fit ◽  
General Extreme Value

Study the statistical distribution for rainfall is important to know the behaviour of the rainfall series and to know the most frequently rainfall amount in each month. Five statistical distribution were applied on Sulaimani, Erbil and Duhok rainfall series for the period (1941-2017) except Duhok (1944-2017). These distributions were Gamma(3P), Weibul(3P), Earlang (3P), Normal and General extreme value. Kolmogrove-Semirnov, Anderson-Darling and Chi-Square goodness of fit test were used to know the best fit distribution from these five distributions.

scholarly journals The Use of Monte Carlo Method to Model the Aggregate Loss Distribution

2020 ◽  
Vol 11 (1) ◽  
pp. 179-190
Author(s):  
Rafika Septiany ◽  
Berlian Setiawaty ◽  
I Gusti Putu Purnaba
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Chi Square ◽  
Loss Distribution ◽  
The Monte Carlo Method ◽  
Chi Square Test ◽  
Claim Frequency ◽  
Aggregate Loss ◽  
Aggregate Loss Distribution ◽  
Anderson Darling

Based on Law Number 24 of 2011, a state program was established to provide social protection and welfare for everyone, one of which is health insurance by the Social Insurance Administration Organization (BPJS). In its implementation, several important evaluations are needed. One that requires accurate evaluation is claim frequency and claim severity in determining premiums and reserved funds. This thesis provides one form of a method for selecting the distribution of claim frequency and claim severity. The data used in this study was taken from BPJS Health in the City of Tangerang in 2017. The distribution of opportunities chosen had been adjusted to the participant's claim data and parameter estimated using the Maximum Likelihood Estimation method. The chi-square test was used to check the goodness of fit for claim frequency distributions whereas the Anderson Darling tests were applied to claim severity distributions. The results of the chi-square test and the Anderson-Darling test showed that the model that matched the claim frequency distribution was the Z12M–NBGE distribution while the model that matched the claim severity was lognormal. The Z12M–NBGE distribution and the lognormal formed the aggregate loss distribution using the Monte Carlo method. Furthermore, the simulation results were obtained to the measurement of the Value in Risk (VaR) and Shortfall Expectations (ES). So, the Monte Carlo method is simple to implement the aggregate loss distributions and can easily handle various risks with dependency.  

scholarly journals Distribuições de probabilidade para séries históricas mensais de pressão atmosférica no município de Mossoró-RN

2016 ◽  
Vol 11 (2) ◽  
pp. 135
Author(s):  
Janilson Pinheiro de Assis ◽  
Roberto Pequeno de Sousa ◽  
Paulo César Ferreira Linhares ◽  
Thiago Alves Pimenta ◽  
Elcimar Lopes da Silva
Keyword(s):  
Atmospheric Pressure ◽  
Probability Distributions ◽  
Probability Density Distribution ◽  
Chi Square ◽  
Pearson Type ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Log Normal ◽  
Von Mises ◽  
Cramer Von Mises

<p>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 H<sub>0</sub>, 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.</p><p align="center"><strong><em>Probability distributions for historic series of monthly atmospheric pressure </em></strong><strong><em>in city</em></strong><strong><em> of Mossoró-RN</em></strong></p><p><strong>Abstract</strong><strong>: </strong>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.</p>

scholarly journals Two Studies in Automobile Insurance Ratemaking

1960 ◽  
Vol 1 (4) ◽  
pp. 192-217 ◽  
Author(s):  
Robert A. Bailey ◽  
LeRoy J. Simon
Keyword(s):  
The Other ◽  
Actual Data ◽  
Automobile Insurance ◽  
Chi Square ◽  
Canadian Experience ◽  
Multiple Classification ◽  
Chi Square Test ◽  
Best Fit ◽  
Improved Methods ◽  
Do So

Section A of this paper uses the Canadian experience for private passenger automobiles to show (1) that merit rating is almost as effective as the class plan in separating the better risks from the poorer risks, (2) that both merit rating and class rating leave unanalyzed a considerable amount of variation among risks and (3) that certain available evidence supports the conclusion that annual mileage, which has long been felt to be an important measure of hazard, is a very significant cause of this unanalyzed variation among risks.Section B presents a method for obtaining relativities among groups on which a multiple classification system has been imposed. The customary method of calculating class relativities uses the total experience for each class with all subdivisions within the classes added together. With the customary method it is difficult to make a completely accurate adjustment for different distributions by territory or merit rating, because any change in the class relativities disturbs the other sets of relativities and conversely. It is shown that even if such an adjustment were made, the customary method of calculating relativities one set at a time does not reflect the relative credibility of each subgroup and does not produce the best fit to the actual data. Moreover it produces differences between the actual data and the fitted values which are far too large to be caused by chance. In addition, for private passenger automobile insurance in Canada, it is shown that two sets of relativities which are multiplied together cannot produce the best fit to the actual data, and some of the consequences of trying to do so are explained. Some methods are advanced whereby all sets of relativities for classes, merit ratings, territories, and so forth, can be calculated simultaneously, which will overcome all the deficiencies in the customary method. These improved methods use the technique of minimizing a measure (technically known as the chi-square test) of the differences between the actual data and the fitted values. Some applications to other lines of insurance are mentioned.

scholarly journals Evaluation of probability distributions in the analysis of minimum temperature series in Manaus – AM

2021 ◽  
Vol 10 (3) ◽  
pp. e46210313616
Author(s):  
Yana Miranda Borges ◽  
Breno Gabriel da Silva ◽  
Brian Alvarez Ribeiro de Melo ◽  
Robério Rebouças da Silva
Keyword(s):  
Probability Distributions ◽  
Information Criterion ◽  
Biological Species ◽  
Temperature Series ◽  
Likelihood Method ◽  
Historical Temperature ◽  
Anderson Darling ◽  
Log Normal ◽  
Von Mises ◽  
Best Fit

The relevance in studying climatological phenomena is based on the influence that variables of this nature exert on the world. Among the most observed variables, temperature stands out, whose effect of its variation may cause significant impacts, such as the proliferation of biological species, agricultural production, population health, etc. Probability distributions have been studied to verify the best fit to describe and/or predict the behavior of climate variables and, in this context, the present study evaluated, among six probability distributions, the best fit to describe a historical temperature series. minimum monthly mean. The series used in this study encompass a period of 38 years (1980 to 2018) separated by month from the weather station of the Manaus - AM station (OMM: 82331) obtained from INMET, totaling 459 observations. Difference-Sign and Turning Point tests were used to verify data independence and the maximum likelihood method to estimate the parameters. Kolmogorov-Smirnov, Anderson-Darling, Cramér-von Mises, Akaike Information Criterion and quantile-quantile plots were used to select the best fit distribution. Log-Normal, Gama, Weibull, Gumbel type II, Benini and Rice distributions were evaluated, with the best performing Rice, Log-Normal and Gumbel II distributions being highlighted.

scholarly journals Equilibrium isotherm studies for the sorption of Nickel ions onto coal fly ash

2014 ◽  
Vol 15 (1&2) ◽  
pp. 153-159
Author(s):  
Ajay K. Agarwal ◽  
Mahendra S. Kadu ◽  
Chandrashekhar P. Pandhurnekar ◽  
Ishwardas L. Muthreja
Keyword(s):  
Fly Ash ◽  
Adsorption Isotherm ◽  
Coal Fly Ash ◽  
Coefficient Of Determination ◽  
Equilibrium Isotherm ◽  
Chi Square ◽  
Linear Coefficient ◽  
Nickel Ions ◽  
Chi Square Test ◽  
Best Fit

The objective of the present study was to study equilibrium isotherm for the sorption of Nickel ions onto coal fly ash. In this study, BET adsorption isotherm was found to be best fitted among  Langmuir, Freundlich, BET, Temkin and Harkins Jura adsorption isotherms using lest square fit method. The best fit adsorption isotherm   is assessed by the linear coefficient of determination (R2) and non-linear Chi-square test. The theoretical value of qe calculated from the best fit linear equation of each adsorption isotherm and the experimental values of qe (0.08) are plotted against Ce, to compare the experimental and Theoretical value of qe.

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