Frequency analysis of low flows using the Akaike information criterion

1996 ◽  
Vol 23 (6) ◽  
pp. 1180-1189 ◽  
Author(s):  
Semiu A. Lawal ◽  
W. Edgar Watt
Keyword(s):  
Lower Bound ◽  
Frequency Analysis ◽  
Akaike Information Criterion ◽  
Goodness Of Fit ◽  
Current Practice ◽  
Information Criterion ◽  
Low Flow ◽  
Parameter Distribution ◽  
Two Parameter ◽  
Parameter Distributions

It is the current practice in frequency analysis of low flows to consider only three-parameter distributions in which one of the parameters represents a nonzero lower bound. When applied to the small samples typically available, this practice results in incorrect low flow estimates. These errors are related to errors in the estimated lower bound. To preclude this possibility, it is proposed that the current practice be changed to include the selection of a two-parameter distribution in certain situations. To assess this proposal, the Akaike information criterion (AIC) is used to compare the suitability of the most commonly used three-parameter distribution (three-parameter Weibull) and three two-parameter distributions (two-parameter Weibull, Gumbel, and lognormal) to low flow data for 51 long-term hydrometric stations across Canada. For 75% of the stations, a two-parameter distribution is selected over the three-parameter distribution if the selection criterion is minimum AIC. In about one third of the remaining 25% of the stations where the three-parameter Weibull distribution gave the minimum AIC, the estimated lower bound is sufficiently close to the minimum observed low flow to indicate overfitting and hence unreliable quantile estimates. When the AIC is supplemented with visual examination of goodness of fit on probability plots, it is found that the lognormal distribution could very well fit those cases where the AIC selected the three-parameter Weibull distribution. Key words: low flow frequency, goodness of fit, information criterion, probability plot.

scholarly journals Discrimination between a group of three-parameter distributions for hydro-meteorological frequency modeling

2018 ◽  
Vol 45 (5) ◽  
pp. 351-365 ◽  
Author(s):  
Ismaila Ba ◽  
Fahim Ashkar
Keyword(s):  
Correlation Coefficient ◽  
Akaike Information Criterion ◽  
Bayesian Information Criterion ◽  
Goodness Of Fit ◽  
Information Criterion ◽  
Extreme Value ◽  
Generalized Extreme Value ◽  
Discrimination Power ◽  
Pearson Type ◽  
Parameter Distributions

We recommend methods of discrimination between some three-parameter distributions used in hydro-meteorological frequency modeling. Discriminations are between model pairs belonging to the group (generalized extreme value (GEV), Pearson Type III (P3), generalized logistic (GLO)). To assess the fit of these distributions to data, the Akaike information criterion, Bayesian information criterion, and (or) goodness-of-fit measures are commonly employed. However, it is difficult to estimate the discrimination power and bias of these methods when used with three-parameter distributions. Consequently, we propose two alternative tools and assess their performance. Both tools are based on a sample transformation to normality followed by applying a powerful statistic for testing normality, such as the Shapiro-Wilk or the probability plot correlation coefficient statistic. While arriving at recommendations for discriminating between the (GEV, GLO) and (P3, GLO) pairs of models, we show that the discrimination power between the P3 and GEV distributions can be rather low.

scholarly journals Statistical Inference of Odd Fréchet Inverse Lomax Distribution with Applications

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
Ramadan A. ZeinEldin ◽  
Muhammad Ahsan ul Haq ◽  
Sharqa Hashmi ◽  
Mahmoud Elsehety ◽  
M. Elgarhy
Keyword(s):  
Goodness Of Fit ◽  
Continuous Distribution ◽  
Information Criterion ◽  
Value Theory ◽  
Estimation Methods ◽  
Parameter Distribution ◽  
Monte Carlo Simulation Study ◽  
Lifetime Distributions ◽  
Lomax Distribution ◽  
Inverse Lomax Distribution

In this article, we propose and study a new three-parameter distribution, called the odd Fréchet inverse Lomax (OFIL) distribution, derived by combining the odd Fréchet-G family and the inverse Lomax distribution. Since Fréchet is a continuous distribution with wide applicability in extreme value theory, the new model contains these properties as well as the characteristics of the inverse Lomax distribution which make it more flexible and provide a good alternative for some well-known lifetime distributions. We initially present a linear representation of its functions and discussion on density and hazard rate function. Then, we study its various mathematical properties. Different estimation methods are used to estimate parameters of OFIL. The Monte Carlo simulation study is carried out to compare the efficiencies of different methods of estimation. The maximum likelihood estimation (MLE) method is used to estimate the OFIL parameters by considering three practical data applications. We show that the related model is the best in comparisons based on Akaike information criterion (AIC), Bayesian information criterion (BIC), and other goodness-of-fit measures.

scholarly journals Modelling the COVID-19 Mortality Rate with a New Versatile Modification of the Log-Logistic Distribution

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Abdisalam Hassan Muse ◽  
Ahlam H. Tolba ◽  
Eman Fayad ◽  
Ola A. Abu Ali ◽  
M. Nagy ◽  
...  
Keyword(s):  
Mortality Rate ◽  
Goodness Of Fit ◽  
Likelihood Estimation ◽  
Cumulative Distribution ◽  
Logistic Distribution ◽  
Parameter Distribution ◽  
Unknown Parameters ◽  
Failure Rate Function ◽  
Competing Models ◽  
Two Parameter

The goal of this paper is to develop an optimal statistical model to analyze COVID-19 data in order to model and analyze the COVID-19 mortality rates in Somalia. Combining the log-logistic distribution and the tangent function yields the flexible extension log-logistic tangent (LLT) distribution, a new two-parameter distribution. This new distribution has a number of excellent statistical and mathematical properties, including a simple failure rate function, reliability function, and cumulative distribution function. Maximum likelihood estimation (MLE) is used to estimate the unknown parameters of the proposed distribution. A numerical and visual result of the Monte Carlo simulation is obtained to evaluate the use of the MLE method. In addition, the LLT model is compared to the well-known two-parameter, three-parameter, and four-parameter competitors. Gompertz, log-logistic, kappa, exponentiated log-logistic, Marshall–Olkin log-logistic, Kumaraswamy log-logistic, and beta log-logistic are among the competing models. Different goodness-of-fit measures are used to determine whether the LLT distribution is more useful than the competing models in COVID-19 data of mortality rate analysis.

scholarly journals A New Lifetime Distribution and Its Power Transformation

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Ammar M. Sarhan ◽  
Lotfi Tadj ◽  
David C. Hamilton
Keyword(s):  
Maximum Likelihood ◽  
Failure Rate ◽  
Real Data ◽  
Parameter Distribution ◽  
Power Transformation ◽  
Unknown Parameters ◽  
Failure Rate Function ◽  
The One ◽  
Two Parameter ◽  
Parameter Distributions

New one-parameter and two-parameter distributions are introduced in this paper. The failure rate of the one-parameter distribution is unimodal (upside-down bathtub), while the failure rate of the two-parameter distribution can be decreasing, increasing, unimodal, increasing-decreasing-increasing, or decreasing-increasing-decreasing, depending on the values of its two parameters. The two-parameter distribution is derived from the one-parameter distribution by using a power transformation. We discuss some properties of these two distributions, such as the behavior of the failure rate function, the probability density function, the moments, skewness, and kurtosis, and limiting distributions of order statistics. Maximum likelihood estimation for the two-parameter model using complete samples is investigated. Different algorithms for generating random samples from the two new models are given. Applications to real data are discussed and compared with the fit attained by some one- and two-parameter distributions. Finally, a simulation study is carried out to investigate the mean square error of the maximum likelihood estimators, the coverage probability, and the width of the confidence intervals of the unknown parameters.

scholarly journals Validação da estrutura fatorial do Körperkoordination Test für Kinder (KTK) em escolares de 8 a 10 anos

2020 ◽  
Vol 8 (3) ◽  
pp. 31
Author(s):  
João Otacilio Libardoni Dos Santos ◽  
Pâmella De Medeiros ◽  
Fernando Luiz Cardoso ◽  
Nilton Soares Formiga ◽  
Nayara Christine Souza ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Akaike Information Criterion ◽  
Goodness Of Fit ◽  
Cross Validation ◽  
Information Criterion ◽  
Mean Square ◽  
Fit Index ◽  
Close Fit

Objetivo: Avaliar a estrutura fatorial do teste KTK em crianças em idade escolar, na faixa etária entre 8 e 10 anos, com base na estrutura unifatorial do KTK. Método: Foram avaliados 350 escolares da cidade de Manaus-AM com idade entre 8 e 10 anos de ambos os sexos. Para análise dos dados considerou-se como entrada, a matriz de covariância, tendo sido adotado o estimador ML (Maximum-Likelihood). Foram utilizados os seguintes indicadores: χ²/gl (qui-quadrado e grau de liberdade), Goodness-of-Fit Index (GFI), Adjusted Goodness-of-Fit Index (AGFI), Root-Mean-Square Error of Approximation (RMSEA), p de Close Fit (PCLOSE), Comparative Fit Index (CFI), Expected Cross-Validation Index (ECVI) e o Consistent Akaike Information Criterion (CAIC). Resultados: A análise fatorial confirmou o modelo unifatorial original da bateria de testes. Deixando livre as covariâncias (phi, φ) entre os itens, os resultados revelaram que os indicadores de qualidade de ajuste são aceitáveis para o modelo proposto, o qual é composto por quatro itens distribuídos em um único fator (χ²/gl = 1.09; GFI = 0.99; AGFI = 0.94; CFI = 0.97; TLI = 0.92; RMSEA = 0.07; PCLOSE = 0.10). Observou-se ainda que todas as saturações (Lambdas, λ), tanto estiveram dentro do intervalo esperado |0 - 1| quando foram estatisticamente diferentes de zero (t > 1.96, p < 0.05). Conclusões: Foi possível identificar aceitáveis evidências de validade baseada na estrutura interna do KTK proposto pelos autores originais confirmando a sua capacidade de investigar e classificar o nível de coordenação motora de crianças, identificando possíveis perturbações ou insuficiências na população avaliada.

scholarly journals Accuracies and Contrasts of Models of the Diffusion-weighted-dependent Attenuation of the Mri Signal at Intermediate B-values

2015 ◽  
Vol 8 ◽  
pp. MRI.S25301 ◽  
Author(s):  
Renaud Nicolas ◽  
Igor Sibon ◽  
Bassem Hiba
Keyword(s):  
White Matter ◽  
Akaike Information Criterion ◽  
Goodness Of Fit ◽  
Information Criterion ◽  
Exponential Model ◽  
B Values ◽  
Diffusion Weighted ◽  
Monoexponential Model ◽  
Biexponential Model ◽  
The Brain

The diffusion-weighted-dependent attenuation of the MRI signal E( b) is extremely sensitive to microstructural features. The aim of this study was to determine which mathematical model of the E( b) signal most accurately describes it in the brain. The models compared were the monoexponential model, the stretched exponential model, the truncated cumulant expansion (TCE) model, the biexponential model, and the triexponential model. Acquisition was performed with nine b-values up to 2500 s/mm2 in 12 healthy volunteers. The goodness-of-fit was studied with F-tests and with the Akaike information criterion. Tissue contrasts were differentiated with a multiple comparison corrected nonparametric analysis of variance. F-test showed that the TCE model was better than the biexponential model in gray and white matter. Corrected Akaike information criterion showed that the TCE model has the best accuracy and produced the most reliable contrasts in white matter among all models studied. In conclusion, the TCE model was found to be the best model to infer the microstructural properties of brain tissue.

scholarly journals A New Goodness-of-Fit Test for the Two-Parameter Gamma Distribution

2022 ◽  
Vol 3 (1) ◽  
pp. 01-06
Author(s):  
Mbanefo S. Madukaife
Keyword(s):  
Gamma Distribution ◽  
Goodness Of Fit ◽  
Critical Values ◽  
Parameter Distribution ◽  
Goodness Of Fit Test ◽  
Gamma Distributions ◽  
Two Parameter

This paper proposes a new goodness-of-fit for the two-parameter distribution. It is based on a function of squared distances between empirical and theoretical quantiles of a set of observations being hypothesized to have come from the gamma distribution. The critical values of the proposed statistic are evaluated through extensive simulations of the unit-scaled gamma distributions and computations. The empirical powers of the statistic are obtained and compared with some well-known tests for the gamma distribution, and the results show that the proposed statistic can be recommended as a test for the gamma distribution.

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 101 Evaluation of Growth Curve Functions for predicted weight in small holder crossbred dairy cattle in Tanzania

2020 ◽  
Vol 98 (Supplement_4) ◽  
pp. 79-80
Author(s):  
Chinyere Ekine ◽  
Raphael Mrode ◽  
Edwin Oyieng ◽  
Daniel Komwihangilo ◽  
Gilbert Msuta ◽  
...  
Keyword(s):  
Growth Curve ◽  
Model Comparison ◽  
Predictive Ability ◽  
Nonlinear Least Squares ◽  
Information Criterion ◽  
Dairy Farms ◽  
Exponential Model ◽  
Males And Females ◽  
Small Holder ◽  
Two Parameter

Abstract Modelling the growth curve of animals provides information on growth characteristics and is important for optimizing management in different livestock systems. This study evaluated the growth curves of crossbred calves from birth to 30 months of age in small holder dairy farms in Tanzania using a two parameter (exponential), four different three parameters (Logistic, von Bertalanffy, Brody, Gompertz), and three polynomial functions. Predicted weights based on heart girth measurements of 623 male and 846 female calves born between 2016 and 2019 used in this study were from the African Dairy Genetic Gains (ADGG) project in selected milk sheds in Tanzania, namely Tanga, Kilimanjaro, Arusha, Iringa, Njomba and Mbeya. Each function was fitted separately to weight measurement of males and females adjusted for the effect of ward and season of birth using the nonlinear least squares (nls) functions in R statistical software. The Akaike’s information criterion (AIC) and Bayesian information criterion (BIC) were used for model comparison. Based on these criteria, all three polynomial and four parameter functions performed better and did not differ enough from each other in both males and females compared to the two-parameter exponential model. Predicted weight varied among the models and differed between males and females. The highest estimated weight was observed in the Brody model for both males (278.09 kg) and females (264.10 kg). Lowest estimated weight was observed in the exponential model. Estimated growth rate varied among models. For males, it ranged from 0.04 kg-0.08 kg and for females, from 0.05 kg-0.09 kg in the Brody model and logistic model respectively. Predictive ability across all fitted curves was low, ranging from 25% to approximately 29%. This could be due to the huge range of breed compositions in the evaluated crossbred calves which characterizes small holder dairy farms in this system and different levels of farm management.

scholarly journals Comparison of growth models to describe growth from birth to 6 years in a Beninese cohort of children with repeated measurements

BMJ Open ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. e035785
Author(s):  
Shukrullah Ahmadi ◽  
Florence Bodeau-Livinec ◽  
Roméo Zoumenou ◽  
André Garcia ◽  
David Courtin ◽  
...  
Keyword(s):  
Growth Model ◽  
Goodness Of Fit ◽  
Growth Models ◽  
Information Criterion ◽  
Height Growth ◽  
Sub Saharan Africa ◽  
Individual Growth ◽  
Secondary Outcome ◽  
Growth Trajectories ◽  
Best Fitting

ObjectiveTo select a growth model that best describes individual growth trajectories of children and to present some growth characteristics of this population.SettingsParticipants were selected from a prospective cohort conducted in three health centres (Allada, Sekou and Attogon) in a semirural region of Benin, sub-Saharan Africa.ParticipantsChildren aged 0 to 6 years were recruited in a cohort study with at least two valid height and weight measurements included (n=961).Primary and secondary outcome measuresThis study compared the goodness-of-fit of three structural growth models (Jenss-Bayley, Reed and a newly adapted version of the Gompertz growth model) on longitudinal weight and height growth data of boys and girls. The goodness-of-fit of the models was assessed using residual distribution over age and compared with the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The best-fitting model allowed estimating mean weight and height growth trajectories, individual growth and growth velocities. Underweight, stunting and wasting were also estimated at age 6 years.ResultsThe three models were able to fit well both weight and height data. The Jenss-Bayley model presented the best fit for weight and height, both in boys and girls. Mean height growth trajectories were identical in shape and direction for boys and girls while the mean weight growth curve of girls fell slightly below the curve of boys after neonatal life. Finally, 35%, 27.7% and 8% of boys; and 34%, 38.4% and 4% of girls were estimated to be underweight, wasted and stunted at age 6 years, respectively.ConclusionThe growth parameters of the best-fitting Jenss-Bayley model can be used to describe growth trajectories and study their determinants.

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