scholarly journals Evaluation of Best-Fit Probability Distribution Models for the Prediction of Inflows of Kainji Reservoir, Niger State, Nigeria

2017 ◽  
Vol 10 ◽  
pp. 117862211769103
Author(s):  
Mohammed J Mamman ◽  
Otache Y Martins ◽  
Jibril Ibrahim ◽  
Mohammed I Shaba
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Type I ◽  
Distribution Models ◽  
Goodness Of Fit Test ◽  
Hydropower Dams ◽  
Log Normal ◽  
Near Future ◽  
Best Fit ◽  
Analysis Of Time Series

The analysis of time series is essential for building mathematical models to generate synthetic hydrologic records, to forecast hydrologic events, to detect intrinsic stochastic characteristics of hydrologic variables, as well as to fill missing and extend records. To this end, various probability distribution models were fitted to river inflows of Kainji Reservoir in New Bussa, Niger State, Nigeria. This is to evaluate the probability function that is best suitable for the prediction of their values and subsequently using the best model to predict for both the expected maximum and minimum monthly inflows at some specific return periods. Three models, ie, Gumbel extreme value type I (EVI), log-normal (LN), and normal (N), were evaluated for the inflows and the best model was selected based on the statistical goodness-of-fit test. The values of goodness-of-fit test for Kainji hydropower dam are as follows: r = 0.96, R2 = 0.99, SEE = 0.0087, χ2 = 0.0054, for Gumbel (EVI); r = 0.79, R2 = 0.85, SEE = 0.02, χ2 = 0.31 for LN; and r = 0.0.75, R2 = 0.0.68, SEE = 0.056, χ2 = 1376.39 for N. For the Kainji hydropower dams, the Gumbel (EVI) model gave the best fit. These probability distribution models can be used to predict the near-future reservoir inflow at the Kainji hydropower dams.

Prediction of Haemoglobin Level by Some Probability Distribution

2020 ◽  
Vol 9 (1) ◽  
pp. 84-88
Author(s):  
Govinda Prasad Dhungana ◽  
Laxmi Prasad Sapkota
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Goodness Of Fit ◽  
Continuous Variable ◽  
Hemoglobin Level ◽  
Chi Square ◽  
Chi Square Test ◽  
Log Normal ◽  
Two Parameters ◽  
Best Fit

 Hemoglobin level is a continuous variable. So, it follows some theoretical probability distribution Normal, Log-normal, Gamma and Weibull distribution having two parameters. There is low variation in observed and expected frequency of Normal distribution in bar diagram. Similarly, calculated value of chi-square test (goodness of fit) is observed which is lower in Normal distribution. Furthermore, plot of PDFof Normal distribution covers larger area of histogram than all of other distribution. Hence Normal distribution is the best fit to predict the hemoglobin level in future.

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 Distribution of Earthquake Magnitude Levels in Bangladesh

2019 ◽  
Vol 11 (3) ◽  
pp. 15
Author(s):  
Md. Habibur Rahman ◽  
Md. Moyazzem Hossain
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Earthquake Magnitude ◽  
Human Beings ◽  
Richter Scale ◽  
Log Normal ◽  
Log Normal Distribution ◽  
Best Fit

Earthquakes are one of the main natural hazards which seriously make threats the life and property of human beings. Different probability distributions of the earthquake magnitude levels in Bangladesh are fitted. In terms of graphical assessment and goodness-of-fit criterion, the log-normal distribution is found to be the best fit probability distributions for the earthquake magnitude levels in Bangladesh among the probability distribution considered in this study. The average earthquake magnitude level found 4.67 (in Richter scale) for log-normal distribution and the approximately forty-six percent chance is predicted to take place earthquake magnitude in the interval four to five.

scholarly journals ​Rainfall Probability Distribution and Forecasting Monthly Rainfall of Navsari using ARIMA Model

2021 ◽  
Author(s):  
D.K. Dwivedi ◽  
P.K. Shrivastava
Keyword(s):  
Probability Distribution ◽  
Stochastic Processes ◽  
Method Of Moments ◽  
Goodness Of Fit ◽  
Moving Average ◽  
Arima Model ◽  
Monthly Rainfall ◽  
Goodness Of Fit Test ◽  
Sowing Time ◽  
Best Fit

Background: Reliable rainfall forecast could be helpful to farmers as major decisions regarding selection of crops and sowing time are based on the rainfall. The univariate time series ARIMA model requires only past data for model formulation and to simulate stochastic processes. The current study was aimed to obtain the probability distribution of monthly rainfall using the method of moments and to forecast rainfall using the ARIMA model. Methods: The method of moments was used to determine the parameters of distributions and the chi-square test was used as a goodness of fit test to obtain the best fit distribution for monthly rainfall of Navsari, Gujarat utilizing 36 years of rainfall data. Auto regressive moving average (ARIMA) model, popular owing to its simplicity and ability to simulate various stochastic processes was used in the study. Result: It was revealed that the Weibull distribution was the best fit distribution for June and September, whereas Gumbel was the best fit distribution for July. For simulating monthly rainfall, the seasonal ARIMA model (0,0,1) (0,1,1)12 was found to be the appropriate model based on its performance. The model had the least root mean square value and also the residuals were found to have no correlation.

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 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 Estimating the Best-Fitted Probability Distribution for Monthly Maximum Temperature at the Sylhet Station in Bangladesh

2021 ◽  
Vol 2 (2) ◽  
pp. 60-67
Author(s):  
Rashidul Hasan Rashidul Hasan
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Probability Model ◽  
Temperature Data ◽  
Maximum Temperature ◽  
Chi Square ◽  
Goodness Of Fit Tests ◽  
Anderson Darling ◽  
Log Normal

The estimation of a suitable probability model depends mainly on the features of available temperature data at a particular place. As a result, existing probability distributions must be evaluated to establish an appropriate probability model that can deliver precise temperature estimation. The study intended to estimate the best-fitted probability model for the monthly maximum temperature at the Sylhet station in Bangladesh from January 2002 to December 2012 using several statistical analyses. Ten continuous probability distributions such as Exponential, Gamma, Log-Gamma, Beta, Normal, Log-Normal, Erlang, Power Function, Rayleigh, and Weibull distributions were fitted for these tasks using the maximum likelihood technique. To determine the model’s fit to the temperature data, several goodness-of-fit tests were applied, including the Kolmogorov-Smirnov test, Anderson-Darling test, and Chi-square test. The Beta distribution is found to be the best-fitted probability distribution based on the largest overall score derived from three specified goodness-of-fit tests for the monthly maximum temperature data at the Sylhet station.

scholarly journals PEMILIHAN DISTRIBUSI PROBABILITAS PADA ANALISA HUJAN DENGAN METODE GOODNESS OF FIT TEST

2016 ◽  
Vol 18 (2) ◽  
pp. 139-148
Author(s):  
Togani Cahyadi Upomo ◽  
Rini Kusumawardani
Keyword(s):  
Normal Distribution ◽  
Goodness Of Fit ◽  
Gumbel Distribution ◽  
Rainfall Event ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Chi Square Test ◽  
Log Normal ◽  
Log Normal Distribution ◽  
Pearson Iii Distribution

Rainfall event is a stochastic process, so to explain and analyze this processes the probability theory and frequency analysisare used. There are four types of probability distributions.They are normal, log normal, log Pearson III and Gumbel. To find the best probabilities distribution, it will used goodness of fit test. The tests consist of chi-square and smirnov-kolmogorov. Results of the chi-square test for normal distribution, log normal and log Pearson III was 0.200, while for the Gumbel distribution was 2.333. Results of Smirnov Kolmogorov test for normal distribution D = 0.1554, log-normal distribution D = 0.1103, log Pearson III distribution D = 0.1177 and Gumbel distribution D = 0.095. All of the distribution can be accepted with a confidence level of 95%, but the best distribution is log normal distribution.Kejadian hujan merupakan proses stokastik, sehingga untuk keperluan analisa dan menjelaskan proses stokastik tersebut digunakan teori probabilitas dan analisa frekuensi. Terdapat empat jenis distribusi probabilitas yaitu distribusi normal, log normal, log pearson III dan gumbel. Untuk mencari distribusi probabilitas terbaik maka akan digunakan pengujian metode goodness of fit test. Pengujian tersebut meliputi uji chi-kuadrat dan uji smirnov kolmogorov. Hasil pengujian chi kuadrat untuk distribusi normal, log normal dan log pearson III adalah 0.200, sedangkan untuk distribusi gumbel 2.333. Hasil pengujian smirnov kolmogorov untuk distribusi normal dengan nilai D = 0.1554, distribusi log normal dengan nilai D = 0.1103, distribusi log pearson III dengan nilai D = 0.1177 dan distribusi gumbel dengan nilai D = 0.095. Seluruh distribusi dapat diterima dengan tingkat kepercayaan 95%, tetapi distribusi terbaik adalah distribusi log normal.

On the use of chi-square analyses in studies of resource utilization

1991 ◽  
Vol 21 (1) ◽  
pp. 58-65 ◽  
Author(s):  
Dennis E. Jelinski
Keyword(s):  
Resource Utilization ◽  
Goodness Of Fit ◽  
Small Sample ◽  
Homogeneity Test ◽  
Type I ◽  
Sample Sizes ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Test Of Homogeneity ◽  
Small Sample Sizes

Chi-square (χ2) tests are analytic procedures that are often used to test the hypothesis that animals use a particular food item or habitat in proportion to its availability. Unfortunately, several sources of error are common to the use of χ2 analysis in studies of resource utilization. Both the goodness-of-fit and homogeneity tests have been incorrectly used interchangeably when resource availabilities are estimated or known apriori. An empirical comparison of the two methods demonstrates that the χ2 test of homogeneity may generate results contrary to the χ2 goodness-of-fit test. Failure to recognize the conservative nature of the χ2 homogeneity test, when "expected" values are known apriori, may lead to erroneous conclusions owing to the increased possibility of committing a type II error. Conversely, proper use of the goodness-of-fit method is predicated on the availability of accurate maps of resource abundance, or on estimates of resource availability based on very large sample sizes. Where resource availabilities have been estimated from small sample sizes, the use of the χ2 goodness-of-fit test may lead to type I errors beyond the nominal level of α. Both tests require adherence to specific critical assumptions that often have been violated, and accordingly, these assumptions are reviewed here. Alternatives to the Pearson χ2 statistic are also discussed.

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