scholarly journals Analyzing the Best Fitted Probabilistic Model for the Seasonal Rainfall Data in Khulna Region of Bangladesh

2021 ◽  
Vol 2 ◽  
pp. 5
Author(s):  
K. Fatema ◽  
Muhammad Habibulla Alamin ◽  
M. Zahid Hasan ◽  
M. Murad Hossain
Keyword(s):  
Goodness Of Fit ◽  
Winter Season ◽  
Monthly Rainfall ◽  
Rainfall Data ◽  
Likelihood Method ◽  
Distribution Model ◽  
Similar Amount ◽  
Post Monsoon ◽  
Goodness Of Fit Tests ◽  
Best Fit

There are several pieces of research on the statistical modeling of rainfall data in Bangladesh. Since all the seasons of a year do not receive a similar amount of rainfall, hence one single statistical model might not be able to explain the pattern of rainfall at any season of a year. According to the climatologists, Bangladesh has four seasons which are Monsoon, Post-monsoon, Summer, and Winter based on the geographical characteristics of this country. This paper aims to determine the best-fitted probability distribution model for the monthly rainfall data of each particular season in the Khulna district of Bangladesh using the rainfall data of the Khulna region from 1951 to 2018. Very commonly used seven continuous distributions- Normal, Weibull, Gamma, Log-normal, Exponential, Cauchy, and Logistic distributions were used to model the data and to evaluate the performances of the distributions, three non-parametric goodness-of-fit tests were conducted, and AIC, BIC values were calculated. Parameters of the distributions were estimated by the maximum likelihood method. The best-fit result of each season was taken as the distribution with the lowest AIC and BIC values. Among the seven distributions, the Gamma distribution showed the best-fit results of the monthly rainfall data for the Monsoon, Post-Monsoon, and Winter Season, and the Weibull distribution showed the best-fit result for Summer Season.

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.

Remaining Useful Life Estimation Based on a Segmental Hidden Markov Model With Continuous Observations

2017 ◽  
Author(s):  
Zhen Chen ◽  
Tangbin Xia ◽  
Ershun Pan
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
Goodness Of Fit ◽  
Hidden Markov ◽  
Remaining Useful Life ◽  
Likelihood Method ◽  
Distribution Model ◽  
Unknown Parameters ◽  
Useful Life ◽  
Hidden States

In this paper, a segmental hidden Markov model (SHMM) with continuous observations, is developed to tackle the problem of remaining useful life (RUL) estimation. The proposed approach has the advantage of predicting the RUL and detecting the degradation states simultaneously. As the observation space is discretized into N segments corresponding to N hidden states, the explicit relationship between actual degradation paths and the hidden states can be depicted. The continuous observations are fitted by Gaussian, Gamma and Lognormal distribution, respectively. To select a more suitable distribution, model validation metrics are employed for evaluating the goodness-of-fit of the available models to the observed data. The unknown parameters of the SHMM can be estimated by the maximum likelihood method with the complete data. Then a recursive method is used for RUL estimation. Finally, an illustrate case is analyzed to demonstrate the accuracy and efficiency of the proposed method. The result also suggests that SHMM with observation probability distribution which is closer to the real data behavior may be more suitable for the prediction of RUL.

Ehrenberg's Negative Binomial Model Applied to Grocery Store Trips

1980 ◽  
Vol 17 (3) ◽  
pp. 385-390 ◽  
Author(s):  
Gil A. Frisbie
Keyword(s):  
Negative Binomial Distribution ◽  
Goodness Of Fit ◽  
Negative Binomial ◽  
Grocery Store ◽  
Distribution Model ◽  
Grocery Stores ◽  
Good Representation ◽  
Binomial Model ◽  
Food Stores ◽  
Goodness Of Fit Tests

Ehrenberg's negative binomial distribution model is applied to a new facet of consumer behavior, the frequency of household filler trips to food stores. Goodness-of-fit tests and intertemporal predictions are assessed. The overall verdict is that the model serves as a good representation of the trips to grocery stores.

Temporal and spatial variations in annual rainfall distribution in Erbil province

2018 ◽  
Vol 47 (1) ◽  
pp. 59-67
Author(s):  
Tariq H Karim ◽  
Dawod R Keya ◽  
Zahir A Amin
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Kendall Test ◽  
Distribution Functions ◽  
Annual Rainfall ◽  
Maximum Rainfall ◽  
Probability Distribution Functions ◽  
Goodness Of Fit Tests ◽  
Annual Maximum Rainfall ◽  
Best Fit

This study aimed to determine the best fit probability distribution of annual maximum rainfall using data from nine stations within Erbil province using different statistical analyses. Nine commonly used probability distribution functions, namely Normal, Lognormal (LN), one-parameter gamma (1P-G), 2P-G, 3P-G, Log Pearson, Weibull, Pareto, and Beta, were assessed. On the basis of maximum overall score, obtained by adding individual point scores from three selected goodness-of-fit tests, the best fit probability distribution was identified. Results showed that the 2P-G distribution and LN distribution were the best fit probability distribution functions for annual rainfall for the region. The analysis of annual rainfall records in Erbil city spanning from 1964 to 2013, covering three periods, also revealed significant temporal changes in the shape and scale parameter patterns of the fitted gamma distribution. Based on the reliable annual rainfall data in the region, the shape and scale parameters were then regionalized, hence it is possible to find the parameter values for any desired location within the study area. The Mann–Kendall test results indicated that there was a decreasing trend in rainfall over most of the study area in recent decades.

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 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.

Fitting The Best–Fit Distribution For The Hourly Rainfall Amount In The Wilayah Persekutuan

2012 ◽  
Author(s):  
Fadhilah Y. ◽  
Zalina Md. ◽  
Nguyen V–T–V. ◽  
Suhaila S. ◽  
Zulkifli Y.
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Rainfall Amount ◽  
Likelihood Method ◽  
Exceedance Probability ◽  
Parameter Estimates ◽  
Goodness Of Fit Test ◽  
Hourly Rainfall ◽  
Best Fit ◽  
Mixed Exponential Distribution

Dalam mengenal pasti model yang terbaik untuk mewakili taburan jumlah hujan bagi data selang masa satu jam di 12 stesen di Wilayah Persekutuan empat taburan digunakan iaitu Taburan Eksponen, Gamma, Weibull dan Gabungan Eksponen. Parameter–parameter dianggar menggunakan kaedah kebolehjadian maksimum. Model yang terbaik dipilih berdasarkan nilai minimum yang diperolehi daripada ujian–ujian kebagusan penyuaian yang digunakan dalam kajian ini. Ujian ini dipertahankan lagi dengan plot kebarangkalian dilampaui. Taburan Gabungan Eksponen di dapati paling baik untuk mewakili taburan jumlah hujan dalam selang masa satu jam. Daripada anggaran parameter bagi taburan Gabungan Eksponen ini, boleh diterjemah bahawa jumlah hujan tertinggi yang direkodkan diperolehi daripada hujan yang dikategorikan sebagai hujan lebat, walaupun hujan renyai–renyai berlaku lebih kerap. Kata kunci: Jumlah hujan dalam selang masa sejam, ujian kebagusan penyuaian, kebolehjadian maksimum In determining the best–fit model for the hourly rainfall amounts for the twelve stations in the Wilayah Persekutuan, four distributions namely, the Exponential, Gamma, Weibull and Mixed–Exponential were used. Parameters for each distribution were estimated using the maximum likelihood method. The best–fit model was chosen based upon the minimum error produced by the goodness–offit tests used in this study. The tests were justified further by the exceedance probability plot. The Mixed–Exponential was found to be the most appropriate distribution in describing the hourly rainfall amounts. From the parameter estimates for the Mixed–Exponential distribution, it could be implied that most of the hourly rainfall amount recorded were received from the heavy rainfall even though there was a high occurrences of light rainfall. Key words: Hourly rainfall amount, goodness-of-fit test, exceedance probability, maximum likelihood

scholarly journals Goodness of Fit Tests in Modeling the Distribution of the Daily Rate of Return of the WIG20 Companies

2012 ◽  
Vol 10 (2) ◽  
pp. 103-113
Author(s):  
Kamila Bednarz
Keyword(s):  
Goodness Of Fit ◽  
Laplace Distribution ◽  
Cumulative Distribution ◽  
Rate Of Return ◽  
Likelihood Method ◽  
Return Distribution ◽  
Chi Square ◽  
Goodness Of Fit Tests ◽  
Daily Rate ◽  
Chi Square Test

Goodness of Fit Tests in Modeling the Distribution of the Daily Rate of Return of the WIG20 Companies In this paper a classic rate of return was examined. Due to a limited quantitative range, the study included only the modeling of the rate of return distribution of the WIG20 index and its companies by means of the Laplace distribution and the Gaussian distribution. Additionally, the goodness of fit tests and methods of estimating the aforementioned distributions parameters were thoroughly covered. When applying the Laplace distribution to modeling the rate of return distribution the parameters were determined by means of two methods: the method of moments and the maximum likelihood method. The maximum period was determined, for which usefulness of the distribution in modeling the rates of return distribution was observed, as well as the results of the chi-square test for class intervals with varying length ensuring equal probability, and for intervals with identical length considering two methods of determining the theoretical size: in accordance with the cumulative distribution function as well as on the basis of the probability density function.

scholarly journals Rainfall trend analysis and its future projection over Gangetic West Bengal (GWB) region of India during post-monsoon and winter season

2016 ◽  
Vol 8 (3) ◽  
pp. 1152-1156 ◽  
Author(s):  
Pramiti Kumar Chakraborty ◽  
Lalu Das
Keyword(s):  
Trend Analysis ◽  
West Bengal ◽  
Winter Season ◽  
Policy Formulation ◽  
Rainfall Data ◽  
Future Projection ◽  
Short Term ◽  
Winter Rainfall ◽  
Post Monsoon ◽  
Increasing Trend

Studying the variability of rainfall and its future projection during post-monsoon and winter season is important for providing the information to the farmers regarding crop planning. For evaluating rainfall scenario, long (1901-2005) and short term (1961-2005 and 1991-2005) rainfall data of nine selected IMD stations of South Bengalwas collected and subdivided into 30 year period up to 1990 and a 15 year period from 1991 to 2005. The data were subjected to trend analysis and available GCM data were compared with the observed rainfall data. The postmonsoon and winter rainfall changes during 1901-2005 were positive (except Krishnangar, -47.67 mm) and negative (except Alipore and Berhampur) respectively. During 1991-2005 all the stations recorded a positive change during post-monsoon, while reverse was true for winter. Among the different GCMs, INGV-ECHM4 estimated the postmonsoon rainfall at the best, whereas winter rainfall successfully estimated by MIROC-Hi. Future projection of both post-monsoon and winter rainfall over the region showed an increasing trend. This will help in policy formulation for water management in agriculture.

scholarly journals Goodness-of-fit tests for the beta Gompertz distribution

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 69-81
Author(s):  
Hanaa Abu-Zinadah ◽  
Asmaa Binkhamis
Keyword(s):  
Goodness Of Fit ◽  
Real Data ◽  
Likelihood Method ◽  
Test Statistics ◽  
Gompertz Distribution ◽  
Goodness Of Fit Tests ◽  
Lilliefors Test ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Von Mises

This article studied the goodness-of-fit tests for the beta Gompertz distribution with four parameters based on a complete sample. The parameters were estimated by the maximum likelihood method. Critical values were found by Monte Carlo simulation for the modified Kolmogorov-Smirnov, Anderson-Darling, Cramer-von Mises, and Lilliefors test statistics. The power of these test statistics founded the optimal alternative distribution. Real data applications were used as examples for the goodness of fit tests.

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