scholarly journals Fitting of Probability Distribution on the Post-Monsoon Rainfall of Different Locations in Bangladesh

2019 ◽  
Vol 9 (2) ◽  
pp. 27
Author(s):  
Md. Habibur Rahman
Keyword(s):  
Probability Distribution ◽  
Weibull Distribution ◽  
Gamma Distribution ◽  
Goodness Of Fit ◽  
Monsoon Rainfall ◽  
Probability Distributions ◽  
Monsoon Precipitation ◽  
Post Monsoon

Different probability distributions of post-monsoon rainfall of different locations in Bangladesh are fitted. It is found that, for the data, Weibull distribution for Barisal, Bogra, Chittagong, Comilla, Cox's Bazar, Faridpur, Jessore, Khulna, Maijdi Court, Mymensingh, Satkhira, and Sylhet; the Gamma distribution for Dhaka, Ishurdi, Rangamati, Rangpur, and Srimangal based on graphical assessment and goodness-of-fit criterion. In this study, different probability distributions have been fitted for the data of post-monsoon precipitation for 17 different locations in Bangladesh over the period 1961-2014.

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 A comparison of three parameter estimation methods of the gamma distribution of annual maximum low flow duration and deficit in the Upper Vistula catchment (Poland)

2018 ◽  
Vol 23 ◽  
pp. 00001
Author(s):  
Katarzyna Baran-Gurgul
Keyword(s):  
Gamma Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Low Flow ◽  
Estimation Methods ◽  
Goodness Of Fit Test ◽  
Flow Duration ◽  
Distribution Parameters ◽  
Anderson Darling ◽  
Parameter Estimation Methods

Based on 30-year 24-hour flow sequences at 69 water gauging stations in the Upper Vistula catchment, it was determined that the probability distributions of the low flow duration and its maximum annual deficit can be described by the gamma distribution with the estimated parameters by the methods: MOM, the method of moments, LMOM, the method of linear moments, and MLE, the method of maximum likelihood. The stationarity of the time series was tested by the Mann-Kendall correlation using the Hamed and Rao variance correction. The low flows were defined by the SPA method, with the limit flow Q70%. The quality of the match was tested by the Anderson-Darling goodness of fit test. This test allowed accepting the gamma distribution in all analysed cases, regardless of the method used to estimate the distribution parameters, since the pv (p-values) values were greater than 5% (over 18% for Tmax and 7.5% for Vmax). The highest pv values for individual water gauging stations, as well as the highest 90% Tmax and Vmax quantiles were noted using LMOM to estimate the gamma distribution parameters. The highest 90% Tmax and Vmax quantiles were observed in the uppermost part of the studied area.

scholarly journals Best Fitted Distribution For Meteorological Data In Kuala Krai

2021 ◽  
Vol 3 (1) ◽  
pp. 16-25
Author(s):  
Siti Mariam Norrulashikin ◽  
Fadhilah Yusof ◽  
Siti Rohani Mohd Nor ◽  
Nur Arina Bazilah Kamisan
Keyword(s):  
Climate Change ◽  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Meteorological Data ◽  
Cumulative Distribution ◽  
Distribution Model ◽  
Data Series ◽  
Distribution Models ◽  
Goodness Of Fit Tests

Modeling meteorological variables is a vital aspect of climate change studies. Awareness of the frequency and magnitude of climate change is a critical concern for mitigating the risks associated with climate change. Probability distribution models are valuable tools for a frequency study of climate variables since it measures how the probability distribution able to fit well in the data series. Monthly meteorological data including average temperature, wind speed, and rainfall were analyzed in order to determine the most suited probability distribution model for Kuala Krai district. The probability distributions that were used in the analysis were Beta, Burr, Gamma, Lognormal, and Weibull distributions. To estimate the parameters for each distribution, the maximum likelihood estimate (MLE) was employed. Goodness-of-fit tests such as the Kolmogorov-Smirnov, and Anderson-Darling tests were conducted to assess the best suited model, and the test's reliability. Results from statistical studies indicate that Burr distributions better characterize the meteorological data of our research. The graph of probability density function, cumulative distribution function as well as Q-Q plot are presented.

scholarly journals Best fitting probability distributions for annual maximum discharge data of the river Kopili, Assam

2009 ◽  
Vol 1 (1) ◽  
pp. 50-52
Author(s):  
Abhijit Bhuyan ◽  
Munindra Borah
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Annual Maximum ◽  
Discharge Data ◽  
Generalized Pareto ◽  
Maximum Discharge ◽  
Pearson Type ◽  
Best Fitting ◽  
Log Normal

In this study our main objective is to determine the best fitting probability distribution for annual maximum flood discharge data of river Kopili, Assam. Various probability distributions i.e. Gumbel (G), generalized extreme value (GEV), normal (N), log-normal (LN3), generalized logistic (GLO), generalized pareto (GPA) and Pearson type-III (PE3) have been used for our study. The L-moments methods have been used for estimating the parameters of all the distributions. The root mean square error (RMSE), model efficiency and D-index (fit in the top six values) together with L-moment ratio diagram is used for goodness of fit measure. It has been observed that Generalized Pareto is the best fitting probability distribution for annual maximum discharge data of river Kopili.

scholarly journals Goodness-of-Fit of Reference Evapotranspiration to Gamma Probability Distribution

2021 ◽  
Vol 13 (6) ◽  
pp. 70
Author(s):  
Janilson Pinheiro de Assis ◽  
Roberto Pequeno de Sousa ◽  
Isaac Reinaldo Pinheiro de Lima ◽  
Paulo César Ferreira Linhares ◽  
Walter Rodrigues Martins ◽  
...  
Keyword(s):  
Probability Distribution ◽  
Gamma Distribution ◽  
Goodness Of Fit ◽  
Reference Evapotranspiration ◽  
Chi Square ◽  
Confidence Levels ◽  
Use Of Data ◽  
Maximum Benefit ◽  
Kolmogorov Smirnov ◽  
Data Period

This paper aims to estimate, using the Penman-Monteith method, the probabilities of reference evapotranspiration (ET0) in millimeters, as well as their accumulated values for ten days (decendial), in Mossoró, northeast Brazil. The Meteorological Station of the Federal Rural University of Semi-Arid (UFERSA) provided the daily records of evapotranspiration. The construction of tables based on the approximation of the variable to the Gamma distribution allows the use of data without transformations. The probabilities were estimated with the Gamma distribution at confidence levels of 1% to 95% over the 1970-2007 data period. The results of the chi-square and Kolmogorov-Smirnov tests at 10% probability (p ≥ 0.10) demonstrated the adequacy of the table construction process, providing essential support in the planning of agricultural activities in the region to obtain the maximum benefit from evapotranspiration data. The Gamma probability distribution best described the ET0 for scaling irrigation systems in the county. The maximum daily ET0 for irrigation projects in the Mossoró region is 10 mm, and the cumulative 10-day ET0 averages 80 mm.

scholarly journals Probability Distribution of Rainfall in Medan

2019 ◽  
Vol 1 (2) ◽  
pp. 43-49 ◽  
Author(s):  
Elly Rosmaini
Keyword(s):  
Probability Distribution ◽  
Gamma Distribution ◽  
Goodness Of Fit ◽  
Monthly Rainfall ◽  
Rainfall Data ◽  
Goodness Of Fit Test ◽  
Normal Distributions ◽  
Lognormal Distributions ◽  
Kolmogorov Smirnov ◽  
Anderson Darling

In this paper we chose three stations in Medan City , Indonesia to estimate Monthly Rainfall Data i.e. Tuntungan, Tanjung Selamat, and Medan Selayang Stations. We took the data from 2007 to 2016. In this case fitted with Normal, Gamma, and Lognormal Distributions. To estimate parameters, we used this method. Furthermore, Kolmogorov-Smirnov and Anderson Darling tests were used the goodness-of-fit test. The Gamma and Normal Distributions is suitable for Tuntungan and Medan Selayang Stations were stated by Kolmogorov-Smirnov's test. Anderson Darling's test stated that Gamma Distribution was suitable for all stations.

scholarly journals Probability Distribution for the Visually Observed Fractional Cloud Cover over the Ocean

2018 ◽  
Vol 31 (8) ◽  
pp. 3207-3232 ◽  
Author(s):  
Marina Aleksandrova ◽  
Sergey K. Gulev ◽  
Konstantin Belyaev
Keyword(s):  
Probability Distribution ◽  
Cloud Cover ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
World Ocean ◽  
Accurate Estimation ◽  
Fractional Cloud ◽  
Low Cloud ◽  
Different Shapes ◽  
Low Cloud Cover

Abstract The authors suggest a three-parameter bounded distribution from the family of mixed gamma distributions for characterizing the probability density distributions of fractional total and low cloud cover over the global oceans. The authors derive both the continuous form of this distribution and its discrete counterpart, which can be directly applied to cloud cover reports. The distribution is applied to the cloud cover characteristics reported by voluntary observing ships (VOS) for the period from 1950 to 2011 after filtering nighttime observations with poor lunar illumination. The suggested distribution demonstrates a high goodness of fit to the data and good skill in capturing probability distributions with different shapes. The authors present seasonal climatologies of the parameters of the derived distribution for the chosen 60-yr period and demonstrate that applying the PDF-based concept to the analysis of cloud cover allows identification of areas where similar mean cloud amounts can be produced by probability distributions with very different shapes. The roles of the different parameters of the distribution in producing the observed cloud conditions in different regions of the World Ocean are discussed. The application of the derived probability distribution allows for accurate estimation of the percentiles of the distribution, which represent the probabilities of specific cloud conditions. These probabilities are presented for both total and low cloud cover, as well as for daytime and nighttime. The authors also discuss the applicability of the suggested distribution for the validation of different cloud cover data products over the globe and the prospects of additional applications.

scholarly journals Probability distributions for explaining hydrological losses in South Australian catchments

2013 ◽  
Vol 17 (11) ◽  
pp. 4541-4553 ◽  
Author(s):  
S. H. P. W. Gamage ◽  
G. A. Hewa ◽  
S. Beecham
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Distribution Functions ◽  
Accurate Estimation ◽  
Rainfall Runoff ◽  
Distribution Fitting ◽  
Distribution Method ◽  
Wide Variability ◽  
Anderson Darling

Abstract. Accurate estimation of hydrological losses is required for making vital decisions in design applications that are based on design rainfall models and rainfall–runoff models. The use of representative single values of hydrological losses, despite their wide variability, is common practice, especially in Australian studies. This practice leads to issues such as over or under estimation of design floods. The probability distribution method is potentially a better technique to describe losses. However, a lack of understanding of how losses are distributed can limit the use of this technique. This paper aims to identify a probability distribution function that can successfully describe hydrological losses of a catchment of interest. The paper explains the systematic process of identifying probability distribution functions, the problems faced during the distribution fitting process and a new generalised method to test the adequacy of fitted distributions. The goodness-of-fit of the fitted distributions are examined using the Anderson–Darling test and the Q–Q plot method and the errors associated with quantile estimation are quantified by estimating the bias and mean square error (MSE). A two-parameter gamma distribution was identified as one that successfully describes initial loss (IL) data for the selected catchments. Further, non-parametric standardised distributions that describe both IL and continuing loss data are also identified. This paper will provide a significant contribution to the Australian Rainfall and Runoff (ARR) guidelines that are currently being updated, by improving understanding of hydrological losses in South Australian catchments. More importantly, this study provides new knowledge on how IL in a catchment is characterised.

scholarly journals Establishment of a Stochastic Model for Sustainable Economic Flood Management in Yewa Sub-Basin, Southwest Nigeria

2016 ◽  
Vol 2 (12) ◽  
pp. 646-655 ◽  
Author(s):  
O.A Agbede ◽  
Oluwatobi Aiyelokun
Keyword(s):  
Probability Distribution ◽  
Stochastic Model ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Flood Management ◽  
Return Periods ◽  
Probability Models ◽  
Goodness Of Fit Test ◽  
Southwest Nigeria ◽  
Anderson Darling

Of all natural disasters, floods have been considered to have the greatest potential damage. The magnitude of economic damages and number of people affected by flooding have recently increased globally due to climate change. This study was based on the establishment of a stochastic model for reducing economic floods risk in Yewa sub-basin, by fitting maximum annual instantaneous discharge into four probability distributions. Daily discharge of River Yewa gauged at Ijaka-Oke was used to establish a rating curve for the sub-basin, while return periods of instantaneous peak floods were computed using the Hazen plotting position. Flood magnitudes were found to increase with return periods based on Hazen plotting position. In order to ascertain the most suitable probability distribution for predicting design floods, the performance evaluation of the models using root mean square error was employed. In addition, the four probability models were subjected to goodness of fit test besed on Anderson-Darling (A2) and Kolmogorov-Smirnov (KS). As a result of the diagnostics test the Weibul probability distribution was confirmed to fit well with the empirical data of the study area. The stochastic model  generated from the Weibul probability distribution, could be used to enhance sustainable development by reducing economic flood damages in the sub-basin.

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