scholarly journals Techniques of quality of adjustment of statistical models with evaluation of probability distributions using production data of laying quails

2021 ◽  
Vol 10 (11) ◽  
pp. e278101119317
Author(s):  
Antonio Augusto Carvas Sant’ Anna ◽  
Jacyara Lopes Pereira ◽  
Matheus Lima Corrêa Abreu ◽  
Adolpho Marlon Antoniol de Moura ◽  
Elon Souza Aniceto ◽  
...  
Keyword(s):  
Akaike Information Criterion ◽  
Probability Distributions ◽  
Information Criterion ◽  
Graphical Analysis ◽  
Cumulative Distribution ◽  
Continuous Data ◽  
Conditional Model ◽  
Anderson Darling ◽  
Von Mises

The goal of our study was to evaluate the quality of fit from different types of probability distributions for continuous data. For this, performance traits and quality of quail egg in the production of nutraceutical eggs were used as a continuous data source. The data were collected over 42 days, the experimental design was completely randomized with 7 treatments, 6 repetitions, with 252 animals allocated in 36 cages. The distributions for continuous data used were the exponential, gamma, gaussian, and lognormal. The R Open Source and SAS® University Edition software was used to perform the analysis. The graphical analysis of the traits was performed from the predicted versus observed values, Cumulative Distribution Function (CDF), and skewness-kurtosis. The fits were also evaluated by the Akaike information criterion (AIC), Bayesian information criterion (BIC), Conditional model of adjusted R-Square (), Conditional model of adjusted concordance correlation (), Kolmogorov-Smirnov test (KS), Cramer-von Mises test (CvM), Anderson-Darling test (AD), Watanabe-Akaike Information Criterion (WAIC) and Leave-one-out cross-validation (LOO). All the tests indicated the Gaussian distribution as the most suitable and they excluded the exponential distribution for all the evaluated characteristics.

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 Effect of Location, Clone, and Measurement Season on the Propagation Velocity of Poplar Trees Using the Akaike Information Criterion for Arrival Time Determination

Materials ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 356
Author(s):  
Francisco Rescalvo ◽  
María Ripoll ◽  
Elisabet Suarez ◽  
Antolino Gallego
Keyword(s):  
Akaike Information Criterion ◽  
Propagation Velocity ◽  
Arrival Time ◽  
Bending Strength ◽  
Information Criterion ◽  
Poplar Trees ◽  
Standing Trees ◽  
Time Determination ◽  
The Waves

The purchase price of any forest plantation depends on the quality of its raw wood, and specifically, variables such as density, orientation of the fibers, bending strength, and bending MoE (Modulus of Elasticity). The elastic waves propagation velocity has become one of the most popular parameters to evaluate the wood in standing trees. This study had two objectives: (1) Show how this velocity is clearly affected by the clone, the location of the crop, and the measurement season of poplar crops; and (2) apply the Akaike information criterion to determinate the arrival time of the waves, on the basis of the entropy of the signals recorded by the piezoelectric sensors placed on the trunk of the tree.

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 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 Simulation of the occurrence of drought events via copulas

RBRH ◽  
2020 ◽  
Vol 25 ◽  
Author(s):  
Rogério de Almeida ◽  
Paulo Sérgio Franco Barbosa
Keyword(s):  
Akaike Information Criterion ◽  
Goodness Of Fit ◽  
Probabilistic Models ◽  
Historical Data ◽  
Probability Distributions ◽  
Information Criterion ◽  
Bivariate Analysis ◽  
Kolmogorov Smirnov ◽  
Hydrological Droughts ◽  
Smirnov Test

ABSTRACT This study presents a method based on Archimedean and Gaussian copulas to simulate the occurrence of hydrological droughts. The droughts were characterized by theory of runs for four threshold levels and six univariate probability distributions were evaluated to represent the probabilistic behavior of their severities and durations. The Akaike Information Criterion was used to select the better univariate probabilistic models, while their hypotheses of goodness-of-fit to the historical data were evaluated by Kolmogorov-Smirnov test. Based on the univariate probability distributions of severities and durations, Archimedean and Gaussian copulas were used in the bivariate analysis of the drought events. The proposed method proves to be a useful tool to simulate the occurrence of drought events, preserving the laws of probability of the severities and durations and the dependency between both.

scholarly journals On Making an Informed Choice between Two Lomax-based Continuous Probability Distributions Using Lifetime Data

2018 ◽  
pp. 1-11 ◽  
Author(s):  
Terna Godfrey Ieren ◽  
Samuel Oluwafemi Oyamakin ◽  
Abubakar Yahaya ◽  
Angela Unna Chukwu ◽  
Adamu Abubakar Umar ◽  
...  
Keyword(s):  
Probability Distributions ◽  
Real Life ◽  
Informed Choice ◽  
Life Situation ◽  
Data Set ◽  
Modeling And Analysis ◽  
Real Life Situation ◽  
Anderson Darling ◽  
Von Mises ◽  
The Right

Probability distributions and their generalisations have contributed greatly in the modeling and analysis of random variables. However, due to the increased introduction of new distributions there has been a major problem with choosing and applying the right distribution for a given set of data. In most cases, it is discovered that the data set in question fits two or more probability distributions and hence one must be chosen among others. The Lomax-Weibull and Lomax-Log-Logistic distributions introduced in an earlier study using a Lomax-based generator were found to be positively skewed and may be victims of this situation especially when modelling positively skewed datasets. In this article, we apply the two distributions to some selected datasets to compare their performance and provide useful insight on how to select the most fit among them when dealing with a real-life situation. We used the log-likelihood value, AIC, CAIC, BIC, HQIC, Cramér-Von Mises (W*) and Anderson Darling (A*) statistics as performance evaluation tools for selecting between the two distributions.

scholarly journals The Type I Quasi Lambert Family

2021 ◽  
pp. 545-558 ◽  
Author(s):  
G. G. Hamedani ◽  
Mustafa C Korkmaz ◽  
Nadeem Shafique Butt ◽  
Haitham M. Yousof
Keyword(s):  
Probability Distributions ◽  
Likelihood Estimation ◽  
Estimation Methods ◽  
Type I ◽  
Unknown Parameters ◽  
Clayton Copula ◽  
New Family ◽  
Renyi’S Entropy ◽  
Anderson Darling ◽  
Von Mises

A new G family of probability distributions called the type I quasi Lambert family is defined and applied for modeling real lifetime data. Some new bivariate type G families using "Farlie-Gumbel-Morgenstern copula", "modified Farlie-Gumbel-Morgenstern copula", "Clayton copula" and "Renyi's entropy copula" are derived. Three characterizations of the new family are presented. Some of its statistical properties are derived and studied. The maximum likelihood estimation, maximum product spacing estimation, least squares estimation, Anderson-Darling estimation and Cramer-von Mises estimation methods are used for estimating the unknown parameters. Graphical assessments under the five different estimation methods are introduced. Based on these assessments, all estimation methods perform well. Finally, an application to illustrate the importance and flexibility of the new family is proposed.

Bootstrap Analysis

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.

DISSONANCE — A MEASURE OF VARIABILITY FOR ORDINAL RANDOM VARIABLES

2001 ◽  
Vol 09 (01) ◽  
pp. 39-53 ◽  
Author(s):  
RONALD R. YAGER
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Probability Distributions ◽  
Random Variables ◽  
Cumulative Distribution ◽  
General Properties

We look at the issue of obtaining a variance like measure associated with probability distributions over ordinal sets. We call these dissonance measures. We specify some general properties desired in these dissonance measures. The centrality of the cumulative distribution function in formulating the concept of dissonance is pointed out. We introduce some specific examples of measures of dissonance.

scholarly journals A Comparison of the Correlation of Systemic Lupus Erythematosus Disease Activity Index 2000 (SLEDAI-2K) and Systemic Lupus Erythematosus Disease Activity Score (SLE-DAS) with Health-Related Quality of Life

2021 ◽  
Vol 10 (10) ◽  
pp. 2137
Author(s):  
Ning-Sheng Lai ◽  
Ming-Chi Lu ◽  
Hsiu-Hua Chang ◽  
Hui-Chin Lo ◽  
Chia-Wen Hsu ◽  
...  
Keyword(s):  
Quality Of Life ◽  
Systemic Lupus Erythematosus ◽  
Disease Activity ◽  
Lupus Erythematosus ◽  
Activity Index ◽  
Disease Activity Index ◽  
Information Criterion ◽  
Systemic Lupus Erythematosus Disease ◽  
Systemic Lupus

Background and Aim: The aim of this study was to compare the correlation of a recently developed systemic lupus erythematosus disease activity score (SLE-DAS) with the SLE disease activity index 2000 (SLEDAI-2K) with the Lupus Quality of Life questionnaire (LupusQoL) in Taiwanese patients with SLE. Methods: A cross-sectional study was conducted in a regional teaching hospital in Taiwan from April to August 2019. Adult patients with a clinician-confirmed diagnosis of SLE based on the 1997 American College of Rheumatology revised criteria or the 2012 Systemic Lupus International Collaborating Clinics Classification Criteria were recruited. SLE disease activity was measured with both SLEDAI-2K and SLE-DAS. Disease-specific quality of life was assessed using the LupusQoL. Results: Of the 333 patients with SLE in this study, 90.4% were female and 40% were between the ages of 20 and 39 years. The median SLEDAI-2K score was 4.00 (interquartile range [IQR] 2.00–7.50) and the median SLE-DAS score was 2.08 (IQR 1.12–8.24) in our patients with SLE. After adjusting for sex and age intervals, both SLEDAI-2k and SLE-DAS were significantly and inversely associated with all eight domains of LupusQoL. The magnitudes of the mean absolute error, root mean square error, Akaike Information Criterion, Bayesian Information Criterion, and coefficient of determination were comparable between SLEDAI-2K and SLE-DAS. Conclusions: There were no clear differences in the use of SLE-DAS over SLEDAI-2K in assessing HRQoL in patients with SLE. We suggest that, in this aspect, both SLEDAI-2K and SLE-DAS are effective tools for measuring disease activity in patients with SLE.

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