Section 2. The X2 - Distribution and the Incomplete Γ- Function: The Pearson Type III Curve; The Poisson Distribution; The Complete Γ- Function and the Factorial; The X2 - Test of Goodness of Fit

2017 ◽  
pp. 130-180
Keyword(s):  
Poisson Distribution ◽  
Goodness Of Fit ◽  
Type Iii ◽  
Pearson Type

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.

scholarly journals Flood Flow Probability Distribution Model Selection on Niger/Benue River Basins in Nigeria

2021 ◽  
pp. 76-94
Author(s):  
Itolima Ologhadien
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
River Basins ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Distribution Model ◽  
Distribution Models ◽  
Type Iii ◽  
Pearson Type ◽  
Best Fit

Flood frequency analysis is a crucial component of flood risk management which seeks to establish a quantile relationship between peak discharges and their exceedance (or non-exceedance) probabilities, for planning, design and management of infrastructure in river basins. This paper evaluates the performance of five probability distribution models using the method of moments for parameter estimation, with five GoF-tests and Q-Q plots for selection of best –fit- distribution. The probability distributions models employed are; Gumbel (EV1), 2-parameter lognormal (LN2), log Pearson type III (LP3), Pearson type III(PR3), and Generalised Extreme Value( GEV). The five statistical goodness – of – fit tests, namely; modified index of agreement (Dmod), relative root mean square error (RRMSE), Nash – Sutcliffe efficiency (NSE), Percent bias (PBIAS), ratio of RMSE and standard deviation of the measurement (RSR) were used to identify the most suitable distribution models. The study was conducted using annual maximum series of nine gauge stations in both Benue and Niger River Basins in Nigeria. The study reveals that GEV was the best – fit distribution in six gauging stations, LP3 was best – fit distribution in two gauging stations, and PR3 is best- fit distribution in one gauging station. This study has provided a significant contribution to knowledge in the choice of distribution models for predicting extreme hydrological events for design of water infrastructure in Nigeria. It is recommended that GEV, PR3 and LP3 should be considered in the development of regional flood frequency using the existing hydrological map of Nigeria.

scholarly journals The propensity to cause accidents

1973 ◽  
Vol 7 (2) ◽  
pp. 154-164 ◽  
Author(s):  
Christoph Haehling von Lanzenauer ◽  
William N. Lundberg
Keyword(s):  
Poisson Distribution ◽  
Automobile Insurance ◽  
Expected Number ◽  
Type Iii ◽  
Pearson Type ◽  
Mean And Variance ◽  
Model Versus ◽  
Image Position ◽  
Binominal Distribution

Information relating to the expected number of losses is of importance in automobile insurance systems. The distribution of risks by number of losses per year may be based on the following model with λ representing the average number of losses per year. This distribution is the Poisson distribution. Tests of this model versus actual observations often indicate significant deviation. This discrepency can result from the constancy of λ which makes the model appropriate for an individual but would require an isohazardous population when applied to a group of individuals. In reality, however, λ will vary from individual to individual. A model accounting for this spread in λ is given in where z(λ) is a distribution describing the spread of λ. The results of model (2) certainly will depend on the form of z(λ). It has been hypothesized that z(λ) can be represented by (3) which is a Pearson Type III [1, 5, 7]. With this assumption model (2) becomes the negative binominal distribution with a mean of and a variance of If the observed mean is and the observed variance it is possible to determine a and b by solving the above equations for mean and variance. Thus and The results indicate an improved fit to actual observations [1, 5, 6].

scholarly journals Comparative Evaluation of Probability Distribution Models of Flood flow in Lower Niger Basin

2021 ◽  
Vol 6 (2) ◽  
pp. 107-117
Author(s):  
Itolima Ologhadien
Keyword(s):  
Water Resources ◽  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Distribution Model ◽  
Distribution Models ◽  
Optimum Distribution ◽  
Water Resources Systems ◽  
Type Iii ◽  
Pearson Type

The choice of optimum probability distribution model that would accurately simulate flood discharges at a particular location or region has remained a challenging problem to water resources engineers. In practice, several probability distributions are evaluated, and the optimum distribution is then used to establish the quantile - probability relationship for planning, design and management of water resources systems, risk assessment in flood plains and flood insurance. This paper presents the evaluation of five probability distributions models: Gumbel (EV1), 2-parameter lognormal (LN2), log pearson type III (LP3), Pearson type III(PR3), and Generalised Extreme Value (GEV) using the method of moments (MoM) for parameter estimation and annual maximum series of five hydrological stations in the lower Niger River Basin in Nigeria. The choice of optimum probability distribution model was made on five statistical goodness – of – fit measures; modified index of agreement (Dmod), relative root mean square error (RRMSE), Nash – Sutcliffe efficiency (NSE), Percent bias (PBIAS), ratio of RMSE and standard deviation of the measurement (RSR), and probability plot correlation coefficient (PPCC). The results show that GEV is the optimum distribution in 3 stations, and LP3 in 2 stations. On the overall GEV is the best – fit distribution, seconded by PR3 and thirdly, LP3. Furthermore, GEV simulated discharges were in closest agreement with the observed flood discharges. It is recommended that GEV, PR3 and LP3 should be considered in the final selection of optimum probability distribution model in Nigeria.

scholarly journals Flood Frequency Analysis of River Niger, Shintaku Gauging Station, Kogi State, Nigeria

2020 ◽  
Vol 5 (2) ◽  
Author(s):  
Andy O Ibeje
Keyword(s):  
Frequency Distribution ◽  
Goodness Of Fit ◽  
Climatic Factors ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Optimal Model ◽  
Frequency Curve ◽  
Type Iii ◽  
Pearson Type ◽  
Niger River

The study outlines a frequency distribution study on the highest annual flood statistics in Niger River located at Shintaku hydrologic Station for period of 58years. In order to determine the optimal model for highest annual flood analysis Generalised extreme value, Log normal, Gumbel maximum, Generalised Pareto and Log Pearson III, were tested. Based on error produced by criteria of goodness of Fit tests, the optimal model was determined. Results obtained indicated that Log Pearson type III was best to model maximum flood magnitude of Niger River at Shintaku station. The flood frequency curve was therefore derived using Log Pearson type III frequency distribution. Flood frequency curve showed that return periods of 50 and 100 years with the probabilities of 2% and1% respectively, yielded discharges of 15300m3/s and 15600m3/s respectively. These results were strongly influenced by their topographical, geographical and climatic factors. The findings of this work will be useful for design engineers in deciding the dimension of hydraulic structures such as spillway, dams, canals, bridges and levees among others. Future studies are required to include flood forecasting in the development of inundation maps for Niger River.Keywords—Return period, Frequency Distribution, Flood, Niger River, Flood Modeling

scholarly journals ASSESSMENT OF THE BEST PROBABILITY DISTRIBUTION METHOD IN RAINFALL FREQUENCY ANALYSIS FOR A TROPICAL REGION

2021 ◽  
Vol 33 (1) ◽  
Author(s):  
Stephen Luo Sheng Yong ◽  
Jing Lin Ng ◽  
Yuk Feng Huang ◽  
Chun Kit Ang
Keyword(s):  
Goodness Of Fit ◽  
Gumbel Distribution ◽  
Tropical Region ◽  
Distribution Method ◽  
Maximum Rainfall ◽  
Significance Level ◽  
Type Iii ◽  
Goodness Of Fit Tests ◽  
Passing Rate ◽  
Pearson Type

The Intensity-Duration-Frequency (IDF) curve defines the relationship between rainfall intensities at certain durations and with the frequencies. The IDF Curve is extensively used in many applications such as flood modelling and peak discharge estimation. Over the years, the frequent occurrence of flood has become a great challenge in Kelantan river basin. Herein, IDF curves using frequency analyses based on different distributions were developed and compared. The historical rainfall data at eight rainfall stations for the period of 1985-2019 were selected for the assessment purpose. The Gumbel, Normal and Log Pearson Type III distributions were fitted into the annual maximum rainfall series for durations varying from 30 minutes to 24 hours. The goodness of fit tests were then used to evaluate the performances of each frequency distribution. It was found that the Gumbel distribution gave the highest passing rate followed by the Log Pearson Type III and then the Normal distributions. The Gumbel distribution resulted in respective 86% and 75% passing rate since most of the p-values generated by both the K-S and the Mann-Whitney test were greater than 5% of significance level leading to the acceptance of the null hypothesis. Thus, the Gumbel distribution is suggested for the frequency analyses in this study.

ESTIMATION OF THE T-YEAR SPECIFIC DISCHARGE USING THE REGIONALISED SKEWNESS COEFFICIENT OF THE LOG-PEARSON TYPE III DISTRIBUTION

2020 ◽  
Author(s):  
Jakub Mészáros ◽  
◽  
Pavol Miklánek ◽  
Pavla Pekárová ◽  
◽  
...  
Keyword(s):  
River Basin ◽  
Type Iii ◽  
River Region ◽  
Pearson Type ◽  
Skewness Coefficient ◽  
Distribution Parameters ◽  
Design Values ◽  
Specific Discharge ◽  
Morava River ◽  
Pearson Type Iii Distribution

In this paper the results are presented of estimation of T-year specific discharge of several streams in two regions in Slovakia. The Qmax time series used in the study were observed at water gauges from lowland Slovak part of the Morava River basin, and from the mountainous Belá River basin. For estimating the design values, we have studied the use of only one type of probability distribution, namely the Log-Pearson Type III Distribution (LP3 distribution). The use of only one type of distribution brings several benefits, e.g. possibility of the regionalization of the distribution parameters (in this study skew coefficient). In the first step the design values of the specific discharge series qmax (with historical data) were estimated and regional skew coefficients Gr of the LP3 distribution were computed. Regional skewness coefficient Gr was estimated to be 0.38 in the Morava River region, and 0.73 in the Belá River region. In many cases the estimate of the 1000-year specific discharge is two times higher than the value of the 100-year specific discharge. Then we have derived the empirical relations between station skew coefficient G and the elevation of the water gauge. In the second step we have derived the empirical relationships between 1000-years specific discharge q1000 and the elevation of the water gauge for both regions separately. The derived empirical regional equations can be used to estimate the 1000-years specific discharge of other streams in the region.

An Empirical Study of an Estimate of Skewness for the Pearson Type III Distribution

1956 ◽  
Vol 10 (2) ◽  
pp. 13
Author(s):  
John Caffrey ◽  
N. C. Perry ◽  
D. Teichroew
Keyword(s):  
Empirical Study ◽  
Type Iii ◽  
Pearson Type ◽  
Pearson Type Iii Distribution
Sign in / Sign up

Export Citation Format

Share Document