Probability Plot Goodness-of-Fit and Skewness Estimation Procedures for the Pearson Type 3 Distribution

1991 ◽  
Vol 27 (12) ◽  
pp. 3149-3158 ◽  
Author(s):  
Richard W. Vogel ◽  
Daniel E. McMartin
Keyword(s):  
Goodness Of Fit ◽  
Probability Plot ◽  
Pearson Type ◽  
Estimation Procedures ◽  
Type 3

scholarly journals Evaluation of Plotting Position Formulae for Pearson Type 3 Distribution in Three Hydrological Stations on the Niger River

2021 ◽  
pp. 117-128
Author(s):  
Itolima Ologhadien
Keyword(s):  
Goodness Of Fit ◽  
Absolute Error ◽  
Distribution Model ◽  
Pearson Type ◽  
Simulated Series ◽  
The Individual ◽  
Individual Scores ◽  
Type 3 ◽  
River Niger ◽  
Relative Root

In this study, eight unbiased plotting position formulae recommended for Pearson Type 3 distribution were evaluated by comparing the simulated series of each formula with the annual maximum series (AMS) of River Niger at Baro, Koroussa and Shintaku hydrological stations, each having data length of 51years, 53 years and 58 years respectively. The parameters of Pearson Type 3 distribution were computed by the method of moments with corrections for skewness. While the fitting of Pearson Type 3 distribution proceeds with the development of flood – return period (Q-T) relationship, followed by application of the derived Q- T relation to compute simulated discharges for comparison with AMS of the study stations. The plotting position formulae were evaluated on the basis of optimum values of the statistically goodness-of-fit of probability plot correlation coefficient (PPCC), relative root mean square error (RRMSE), percent bias (PBIAS), mean absolute error (MAE) and Nash-sutcliffe efficiency (NSE), across the stations. The plotting position formulae were ranked on scale of 1 to 8. Thus a plotting formula that best simulates the empirical observations using the goodness-of-measures was scored “1” and so on. The individual scores per plotting position were summed across the gof tests to obtain the total score.    The study show that Chegodayev is the best plotting position formula for Baro, Weibull is the best plotting position Formula for Kourassou and Shintaku hydrological stations. The overall performances of the eight plotting position formulae across the hydrological stations show that weibull distribution is the overall best having scored 27, seconded by Chegodayev with 30 and thirdly, Beard with 38. The Pearson Type 3 distribution had been found one of the best probability distribution model of flood flow in Nigeria and this study was conducted to gain in-depth knowledge of the distribution. Finally, this study recommends extension of the studies to Log-Pearson Type 3 distribution.

scholarly journals Modelling Rainfall Intensity by Optimization Technique in Abeokuta, South-West, Nigeria

2019 ◽  
pp. 1-10
Author(s):  
A. O. David ◽  
Ify L. Nwaogazie ◽  
J. C. Agunwamba
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Rainfall Intensity ◽  
Mean Squared Error ◽  
Optimization Technique ◽  
Distribution Models ◽  
Goodness Of Fit Test ◽  
Maximum Rainfall ◽  
Pearson Type ◽  
Type 3

The design of water resources engineering control structures is best achieved with adequate estimation of rainfall intensity over a particular catchment. To develop the rainfall intensity, duration and frequency (IDF) models, 25 year daily rainfall data were collected from Nigerian Meteorological Agency (NIMET) Abuja for Abeokuta. The annual maximum rainfall amounts with durations of 5, 10, 15, 20, 30, 45, 60, 90, 120, 180, 240, 300 and 420 minutes were extracted and subjected to frequency analysis using the Excel Optimization Solver wizard. Specific and general IDF models were developed for return periods of 2, 5, 10, 25, 50 and 100 years using the Gumbel Extreme Value Type -1 and Log Pearson Type -3 distributions. The Anderson-Darling goodness of fit test was used to ascertain the best fit probability distribution. The R2 values range from 0.973 – 0.993 and the Mean Squared Error, MSE from 84.49 – 134.56 for the Gumbel and 0.964 – 0.997 with MSE of 42.88 – 118.68 for Log Pearson Type -3 distribution, respectively. The probability distribution models are recommended for the prediction of rainfall intensities for Abeokuta metropolis.

scholarly journals Evaluation of Generalized Extreme (GEV), Log-Pearson Type 3 (LP3), Pearson Type 3(P3) and Gumbel (EV1) Distributions for Development of IDF Equations for Warri, Nigeria

2021 ◽  
pp. 386-395
Author(s):  
Itolima Ologhadien
Keyword(s):  
Goodness Of Fit ◽  
Probability Distributions ◽  
Series Data ◽  
Economic Losses ◽  
Precipitation Series ◽  
Return Periods ◽  
Water Drainage ◽  
Pearson Type ◽  
Idf Curves ◽  
Type 3

The application of Gumbel (EVI) to the development of rainfall intensity– duration – frequency (IDF) curves has often been criticized on theoretical and empirical grounds as it may underestimate the largest extreme rainfall amounts. The consequences of underestimation are economic losses, property damages, and loss of life. Therefore, it is important that water resources engineering infrastructure be accurately design to avoid these consequences. This paper evaluates the performances of four probability distributions; GEV, EV1, LP3 and P3 using the annual maxima precipitation series of 26 years for Warri Metropolis obtained from Nigerian Meteorological Agency (NiMet). The strength and weakness of the four probability distributions were examined with the goodness of fit (GOF) module of Easyfit software which implemented Kolmogorov - Smirnov (KS) and Anderson - Darling (AD) tests at 5% significance level. The Easyfit software fitted the precipitation series data to the four probability distributions and ranked the four probability distributions across the fifteen rainfall durations. Results show that for both KS and AD tests, GEV distribution was found to be best-fit distribution and it was applied to the development of IDF curves in Warri Metropolis, Nigeria. Furthermore, the IDF values obtained were applied in the development of three-parameter IDF models for return periods of 10 - , 15 -, 20 -, 25 - , 50 -, and 100-years. The mean absolute error, Nash – Sutcliffe Efficiency (NSE) and Root Mean Square Error (RMSE) indices computed for the IDF models increase with increasing return periods. The IDF curves and models depicted the general attributes of IDF curves and models. This study could be of significant academic value and improvement to professional practice in the design of storm water drainage systems. Therefore, the developed IDF curves and models are recommended to the Warri Urban Authority for inclusion in her stormwater handbooks and manuals.

scholarly journals Development of Models for Rainfall Intensity- duration-frequency for Akure, South-west, Nigeria

2019 ◽  
pp. 457-466
Author(s):  
A. O. David ◽  
Ify L. Nwaogazie ◽  
J. C. Agunwamba
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Rainfall Intensity ◽  
Mean Squared Error ◽  
Distribution Models ◽  
Goodness Of Fit Test ◽  
Maximum Rainfall ◽  
Pearson Type ◽  
Intensity Duration Frequency ◽  
Type 3

The rainfall Intensity-Duration-Frequency (IDF) relationship is widely used for adequate estimation of rainfall intensity over a particular catchment. A 25 year daily rainfall data were collected from Nigerian Meteorological Agency (NIMET) Abuja for Akure station. Twenty five year annual maximum rainfall amounts with durations of 5, 10, 15, 20, 30, 45, 60, 90, 120, 180, 240, 300 and 420 minutes were extracted and subjected to frequency analysis using the excel solver software wizard. A total of six (6) return period specific and one (1) general IDF models were developed for return periods of 2, 5, 10, 25, 50 and 100 years using Gumbel Extreme Value Type-1 and Log Pearson Type -3 distributions. Anderson Darling goodness of fit test was used to ascertain the best fit probability distribution. The R2 values range from 0.982 to 0.985 for GEVT -1 and 0.978 to 0.989 for Log Pearson type -3 while the Mean Squared Error from 33.56 to 156.50 for GEVT -1 and 43.01 to 150.63 Log Pearson Type III distributions respectively. The probability distribution models are recommended for the prediction of rainfall intensities for Akure metropolis.

scholarly journals A best-fit probability distribution for the estimation of rainfall in northern regions of Pakistan

2016 ◽  
Vol 11 (1) ◽  
pp. 432-440 ◽  
Author(s):  
M. T. Amin ◽  
M. Rizwan ◽  
A. A. Alazba
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Future Research ◽  
Maximum Rainfall ◽  
Type Iii ◽  
Goodness Of Fit Tests ◽  
Pearson Type ◽  
Northern Regions ◽  
Best Fit

AbstractThis study was designed to find the best-fit probability distribution of annual maximum rainfall based on a twenty-four-hour sample in the northern regions of Pakistan using four probability distributions: normal, log-normal, log-Pearson type-III and Gumbel max. Based on the scores of goodness of fit tests, the normal distribution was found to be the best-fit probability distribution at the Mardan rainfall gauging station. The log-Pearson type-III distribution was found to be the best-fit probability distribution at the rest of the rainfall gauging stations. The maximum values of expected rainfall were calculated using the best-fit probability distributions and can be used by design engineers in future research.

scholarly journals MENENTUKAN DISTRIBUSI REPRESENTATIF FREQUENSI CURAHAN HUJAN HARIAN MAKSIMUM DENGAN METODEHISTOGRAM DAN METODE PARAMETIK DI PROVINSI SUMATERA BARAT

2018 ◽  
Vol 1 (1) ◽  
Author(s):  
Selpa Dewi
Keyword(s):  
Goodness Of Fit ◽  
Type Iii ◽  
Pearson Type ◽  
Chi Squared ◽  
Anderson Darling

Penelitian ini bertujuan untuk menentukan distribusi yang representatif frequensi curahan hujan harian maksimum di Provinsi Sumatera Barat. Data yang digunakan untuk penelitian ini diambil dari data hujan maksimum harian selama 20 sampai 40 tahunan, dengan 24 stasiun penakar hujan untuk provinsi Sumatera Barat. Data masing-masing stasiun kemudian disusun dalam dua jenis deret data, yaitu deret data annual maxima dan deret data annual exceedances. Dari hasil uji deret data ini diharapkan mengikuti satu atau beberapa dari distribusi yang umum dipakai dalam hidrologi rekayasa, yaitu distribusi normal, normal-log, Gumbel, Gama-II, Gama-III dan distribusi Log-Pearson Type III (LP-III). Dengan mengunakan uji kecocokan (goodness of fit), uji parametrik, Chi-Squared test, Kolmogorov-Smirnovtest dan Anderson-Darling test ditambah dengan metode histrogram (visual).Kata kunci:Intensitas hujan distribusi representative annual maxima, annual exceendances, goodness of fitprovinsi Sumatera Barat.

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