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 Evaluation of the best fit distribution for partial duration series of daily rainfall in Madinah, western Saudi Arabia

2014 ◽  
Vol 364 ◽  
pp. 159-163 ◽  
Author(s):  
F. Alahmadi ◽  
N. A. Rahman ◽  
M. Abdulrazzak
Keyword(s):  
Saudi Arabia ◽  
Akaike Information Criterion ◽  
Daily Rainfall ◽  
Information Criterion ◽  
Extreme Value ◽  
Generalized Extreme Value ◽  
Partial Duration Series ◽  
Type Iii ◽  
Pearson Type ◽  
Best Fit

Abstract. Rainfall frequency analysis is an essential tool for the design of water related infrastructure. It can be used to predict future flood magnitudes for a given magnitude and frequency of extreme rainfall events. This study analyses the application of rainfall partial duration series (PDS) in the vast growing urban Madinah city located in the western part of Saudi Arabia. Different statistical distributions were applied (i.e. Normal, Log Normal, Extreme Value type I, Generalized Extreme Value, Pearson Type III, Log Pearson Type III) and their distribution parameters were estimated using L-moments methods. Also, different selection criteria models are applied, e.g. Akaike Information Criterion (AIC), Corrected Akaike Information Criterion (AICc), Bayesian Information Criterion (BIC) and Anderson-Darling Criterion (ADC). The analysis indicated the advantage of Generalized Extreme Value as the best fit statistical distribution for Madinah partial duration daily rainfall series. The outcome of such an evaluation can contribute toward better design criteria for flood management, especially flood protection measures.

scholarly journals The application of new distribution in determining extreme hydrologic events such as floods

2020 ◽  
Author(s):  
Łukasz Gruss ◽  
Jaroslav Pollert Jr. ◽  
Jaroslav Pollert Sr. ◽  
Mirosław Wiatkowski ◽  
Stanisław Czaban
Keyword(s):  
Extreme Value ◽  
Generalized Extreme Value Distribution ◽  
Accurate Estimation ◽  
Annual Maximum ◽  
Generalized Extreme Value ◽  
Hill Plot ◽  
Pearson Type ◽  
The Mean ◽  
Parameter Distributions ◽  
Mixed Distributions

Abstract. In hydrology, statistics of extremes play an important role in the use of time series analysis as well as in planning, design and operation of hydrotechnical structures and water systems. In particular, probability distributions are used to estimate and forecast floods. However, in order to use distributions, the data must be random, with a change-point and should not have a trend. Unfortunately, the data being analyzed are not independent, which is very often due to the anthropogenic impact, among other factors. In situations where various processes generate rainfall and floods in river basins, the use of mixed distributions is recommended. However, an accurate estimation of multiple parameters derived from a mixture of distributions can be difficult, which is the biggest disadvantage of this approach. Therefore, as an alternative, we propose a new extension of the GEV distribution – the Dual Gamma Generalized Extreme Value Distribution (GGEV) developed by Nascimento, Bourguignony and Leão (2016). We compared this distribution with selected 3-parameter distributions: Pearson type III, Log-Normal, Weibull and Generalized Extreme Value. In addition, various methods of estimating 3-parameter distributions were used. As a case study, rivers from Poland and the Czech Republic were investigated, because this has a significant impact on water management in the Upper Oder basin due to the strategic water reservoirs and other hydrotechnical constructions, either existing or planned. Currently, there are no clearly indicated distributions for the Upper Oder basin. Therefore, our aim was to approximate them. Two methods were used, namely the Annual Maximum (AM) and the Peaks Over Threshold (POT). In the latter case, two methods for determining the threshold were used, namely: the Mean of the Annual Maximum River Flows (MAMRF) and the Hill plot. Hence, the basic 3-parameter Weibull distribution, with parameters estimated using the modified method of moments and the maximum likelihood estimation, yielded a better fit to the observation series in the AM and POT methods. For the AM and POT (MAMRF, Hill plot) methods, the GGEV turned out to be the best-fitted distribution according to the Mean Absolute Relative Error (MARE). The GGEV distribution can be used as an alternative to mixed distributions in various samples, both homogeneous and heterogeneous. This distribution turned out to be the best fit especially for the sample whose independence is affected by the presence of a GGEV water reservoir.

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 Bicycle Speed Modelling Considering Cyclist Characteristics, Vehicle Type and Track Attributes

2021 ◽  
Vol 12 (1) ◽  
pp. 43
Author(s):  
Xingchen Yan ◽  
Xiaofei Ye ◽  
Jun Chen ◽  
Tao Wang ◽  
Zhen Yang ◽  
...  
Keyword(s):  
Information Criterion ◽  
Lateral Position ◽  
Extreme Value ◽  
Optimal Number ◽  
Generalized Extreme Value ◽  
Vehicle Type ◽  
Lane Width ◽  
Bike Sharing ◽  
Mode Of Transport ◽  
Best Fit

Cycling is an increasingly popular mode of transport as part of the response to air pollution, urban congestion, and public health issues. The emergence of bike sharing programs and electric bicycles have also brought about notable changes in cycling characteristics, especially cycling speed. In order to provide a better basis for bicycle-related traffic simulations and theoretical derivations, the study aimed to seek the best distribution for bicycle riding speed considering cyclist characteristics, vehicle type, and track attributes. K-means clustering was performed on speed subcategories while selecting the optimal number of clustering using L method. Then, 15 common models were fitted to the grouped speed data and Kolmogorov–Smirnov test, Akaike information criterion, and Bayesian information criterion were applied to determine the best-fit distribution. The following results were acquired: (1) bicycle speed sub-clusters generated by the combinations of bicycle type, bicycle lateral position, gender, age, and lane width were grouped into three clusters; (2) Among the common distribution, generalized extreme value, gamma and lognormal were the top three models to fit the three clusters of speed dataset; and (3) integrating stability and overall performance, the generalized extreme value was the best-fit distribution of bicycle speed.

scholarly journals Model Selection Procedures in Bounds Test of Cointegration: Theoretical Comparison and Empirical Evidence

Economies ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 49 ◽  
Author(s):  
Waqar Badshah ◽  
Mehmet Bulut
Keyword(s):  
Model Selection ◽  
Akaike Information Criterion ◽  
Bayesian Information Criterion ◽  
Selection Process ◽  
Information Criterion ◽  
Small Sample ◽  
Information Criteria ◽  
Path Model ◽  
Sample Sizes ◽  
Bounds Test

Only unstructured single-path model selection techniques, i.e., Information Criteria, are used by Bounds test of cointegration for model selection. The aim of this paper was twofold; one was to evaluate the performance of these five routinely used information criteria {Akaike Information Criterion (AIC), Akaike Information Criterion Corrected (AICC), Schwarz/Bayesian Information Criterion (SIC/BIC), Schwarz/Bayesian Information Criterion Corrected (SICC/BICC), and Hannan and Quinn Information Criterion (HQC)} and three structured approaches (Forward Selection, Backward Elimination, and Stepwise) by assessing their size and power properties at different sample sizes based on Monte Carlo simulations, and second was the assessment of the same based on real economic data. The second aim was achieved by the evaluation of the long-run relationship between three pairs of macroeconomic variables, i.e., Energy Consumption and GDP, Oil Price and GDP, and Broad Money and GDP for BRICS (Brazil, Russia, India, China and South Africa) countries using Bounds cointegration test. It was found that information criteria and structured procedures have the same powers for a sample size of 50 or greater. However, BICC and Stepwise are better at small sample sizes. In the light of simulation and real data results, a modified Bounds test with Stepwise model selection procedure may be used as it is strongly theoretically supported and avoids noise in the model selection process.

scholarly journals Identificación de un modelo lineal adecuado para evaluar características pre-destete en ganado criollo colombiano Blanco Orejinegro

2021 ◽  
Vol 26 (1) ◽  
pp. 49-56
Author(s):  
Luisa Fernanda Naranjo Guerrero ◽  
Alberiro López Herrera ◽  
Juan Carlos Rincon Florez ◽  
Luis Gabriel González Herrera
Keyword(s):  
Akaike Information Criterion ◽  
Bayesian Information Criterion ◽  
Information Criterion ◽  
Modelo Lineal

La Raza criolla Blanco Orejinegro (BON) tiene un proceso de adaptación de más de 500 años a las condiciones ambientales de Colombia. Se caracteriza por ser una raza doble propósito utilizada para la producción de leche y carne, convirtiéndola en un patrimonio biológico de gran importancia que debe ser estudiado. El objetivo de este estudio fue identificar un modelo lineal adecuado para evaluar características pre-destete en ganado criollo Blanco Orejinegro. Se recolectó y depuró información de pesajes de cuatro hatos de ganado BON. Las características evaluadas fueron peso a los 4 meses (P4M), peso al destete (PD) y ganancia diaria de peso entre los 4 meses y el destete (GDP4M-D). Se evaluaron nueve modelos lineales en los que se incluyeron como efectos fijos los siguientes factores: sexo, hato, mes de pesaje o nacimiento, número de parto, época de pesaje o época de nacimiento (época seca o lluviosa), edad (covariable, efecto fijo y ajustada por regresión), año de pesaje o año de nacimiento y grupo contemporáneo (GC) compuesto por sexo y hato para GDP4M-D y sexo, hato y año de pesaje para P4M y PD, con mínimo cinco observaciones por GC. Para identificar el modelo lineal más adecuado para cada característica se utilizó el valor de AIC (Akaike information criterion), BIC (Bayesian information criterion), coeficiente de determinación (R2) y la suma de cuadrados del error (SCE). El modelo más adecuado para todas las características fue aquel que involucró el GC y edad como efecto fijo para P4M y edad como covariable para PD.

scholarly journals STATISTICAL INTERPRETATION AND OPTIMIZATION OF VALSARTAN FLOATING TABLETS USING BOX-BEHNKEN DESIGN

2019 ◽  
pp. 44-53
Author(s):  
SANKHA BHATTACHARYA
Keyword(s):  
Akaike Information Criterion ◽  
Bayesian Information Criterion ◽  
Information Criterion ◽  
Stability Study ◽  
Therapeutic Window ◽  
Dissolution Time ◽  
Floating Tablets ◽  
Mean Dissolution Time ◽  
Styrene Divinylbenzene

Objective: The main purpose of this study was to formulate and statistically evaluate 300 mg floating tablets of valsartan. Methods: Floating tablets of valsartan was prepared in 16 station rotary punching machine by considering 300 mg of valsartan as drug, 40-60 mg of hydroxypropyl methylcellulose (HPMC) K100M and 20-40 mg of poly (styrene-divinylbenzene) as polymers and 20 mg of sodium bicarbonate as gas generating agents. Since upper stomach has maximum therapeutic window for valsartan absorption, hence Gastroretentive Floating Tablets (GRFTs) was prepared by implementing Box-Bentham Design. The pre and post compression parameters were optimized using Statistica 10 software. From the in vitro buoyancy and drug release studies and interpretation of statistical outcomes viz. Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Root Mean Squared Error (RMSE), Dissolution Efficiency (DE), Mean Dissolution Time (MDT), desirability study, it was concluded that batch VF5 formulation was found to be the most optimized formulation. Results: The floating time of VF5 was found to be 132±0.33 sec, in vitro buoyancy time was 18 h, Akaike Information Criterion (AIC) was 54.97, Bayesian Information Criterion (BIC) was 5.13, percentage dissolution efficacy was 56.39%, mean dissolution time was 5.19hr. Further, six-month stability study was performed as per ICH QIA guideline. After performing two-way ANOVA within stability study response variables, it was confirmed that the interaction was most significant. Conclusion: Valsartan floating drug delivery system was successfully developed by considering HPMC K100M and poly (styrene-divinylbenzene) as polymers. Among all the nine batches, VF5 was found to be the best-optimized batch.

scholarly journals SEM-PLS Untuk Analisis Struktur Kemiskinan Pada Masa Pandemi Covid-19

2021 ◽  
Vol 2021 (1) ◽  
pp. 195-203
Author(s):  
Rahma Rahma Nuryanti ◽  
Tulus Soebagijo
Keyword(s):  
Akaike Information Criterion ◽  
Structural Equation Modelling ◽  
Bayesian Information Criterion ◽  
Structural Equation ◽  
Information Criterion ◽  
Partial Least Square ◽  
Finite Mixture ◽  
Least Square ◽  
Equation Modelling

Pandemi Covid-19 menimbulkan berbagai dampak khususnya pada aspek perekonomian. Kondisi perekonomian yang sulit ini menyebabkan pendapatan masyarakat mengalami penurunan, dan menyebabkan jumlah penduduk miskin meningkat. Jumlah penduduk miskin bertambah sebanyak 1,28 juta orang pada tahun 2020. Provinsi Jawa Timur merupakan provinsi yang memiliki tingkat kemiskinan (10,20 persen) sedikit lebih tinggi daripada nasional (10,19 persen) pada tahun 2020. Hal ini dikarenakan adanya dampak pandemi yang menyebabkan hilangnya lapangan pekerjaan dan meningkatnya angka kemiskinan. Penelitian ini akan menganalisis struktur kemiskinan di Provinsi Jawa Timur pada tahun 2020. Tujuan penelitian ini adalah untuk melihat struktur kemiskinan di Provinsi Jawa Timur pada tahun 2020.  Metode analisis yang digunakan dalam penelitian ini adalah Structural Equation Modelling (SEM) berbasis komponen yaitu Partial Least Square (PLS). Pada model persamaan struktural terdapat 4 jalur yang signifikan, yaitu pengaruh variabel kesehatan terhadap variabel pendidikan, pengaruh variabel kesehatan dan variabel pendidikan terhadap ekonomi, serta pengaruh variabel ekonomi terhadap variabel kemiskinan. Hasil Analisis Pengelompokan dengan Finite Mixture Partial Least Square berdasarkan kriteria Akaike Information Criterion (AICk), Consistent Akaike Information Criterion (CAICk) dan Bayesian Information Criterion ( BICk) serta Normal Entrophy (EN) diperoleh hasil terbaik yang terbentuk adalah 2 segmen. Sehingga dari 38 kabupaten/kota di wilayah Provinsi Jawa Timur dapat dikelompokkan menjadi 2 segmen. Segmen Pertama sebesar 91,9 persen dari jumlah kabupaten/kota, dan Segmen Kedua sebesar 8,1 persen dari jumlah kabupaten/kota di wilayah Jawa Timur. Kabupaten/kota yang berada pada segmen kedua adalah Kabupaten Situbondo, Kabupaten Nganjuk dan Kota Kediri. Sementara 35 kabupaten/kota lainnya berada di segmen pertama.

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