Statistical Distribution of Rainfall in Kurdistan-Iraq Region

Study the statistical distribution for rainfall is important to know the behaviour of the rainfall series and to know the most frequently rainfall amount in each month. Five statistical distribution were applied on Sulaimani, Erbil and Duhok rainfall series for the period (1941-2017) except Duhok (1944-2017). These distributions were Gamma(3P), Weibul(3P), Earlang (3P), Normal and General extreme value. Kolmogrove-Semirnov, Anderson-Darling and Chi-Square goodness of fit test were used to know the best fit distribution from these five distributions.

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Estimation of flood frequency using statistical method: Mahanadi River basin, India

H2Open Journal ◽

10.2166/h2oj.2020.004 ◽

2020 ◽

Vol 3 (1) ◽

pp. 189-207

Author(s):

Sandeep Samantaray ◽

Abinash Sahoo

Keyword(s):

Stream Flow ◽

Goodness Of Fit ◽

Central India ◽

Extreme Value ◽

Flood Frequency ◽

Goodness Of Fit Test ◽

Mahanadi River ◽

Goodness Of Fit Tests ◽

Study Results ◽

Anderson Darling

Abstract Estimating stream flow has a substantial financial influence, because this can be of assistance in water resources management and provides safety from scarcity of water and conceivable flood destruction. Four common statistical methods, namely, Normal, Gumbel max, Log-Pearson III (LP III), and Gen. extreme value method are employed for 10, 20, 30, 35, 40, 50, 60, 70, 75, 100, 150 years to forecast stream flow. Monthly flow data from four stations on Mahanadi River, in Eastern Central India, namely, Rampur, Sundargarh, Jondhra, and Basantpur, are used in the study. Results show that Gumbel max gives better flow discharge value than the Normal, LP III, and Gen. extreme value methods for all four gauge stations. Estimated flood values for Rampur, Sundargarh, Jondhra, and Basantpur stations are 372.361 m3/sec, 530.415 m3/sec, 2,133.888 m3/sec, and 3,836.22 m3/sec, respectively, considering Gumbel max. Goodness-of-fit tests for four statistical distribution techniques applied in the present study are also evaluated using Kolmogorov–Smirov, Anderson–Darling, Chi-squared tests at critical value 0.05 for the four proposed gauge stations. Goodness-of-fit test results show that Gen. extreme value gives best results at Rampur, Sundergarh, and Jondhra gauge stations followed by LP III, whereas LP III is the best fit for Basantpur, followed by Gen. extreme value.

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

Jurnal Teknologi ◽

10.11113/jt.v46.288 ◽

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

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Expanded Fréchet Model: Mathematical Properties, Copula, Different Estimation Methods, Applications and Validation Testing

Mathematics ◽

10.3390/math8111949 ◽

2020 ◽

Vol 8 (11) ◽

pp. 1949

Author(s):

Mukhtar M. Salah ◽

M. El-Morshedy ◽

M. S. Eliwa ◽

Haitham M. Yousof

Keyword(s):

Maximum Likelihood ◽

Goodness Of Fit ◽

Estimation Method ◽

Least Square ◽

Estimation Methods ◽

Goodness Of Fit Test ◽

Least Square Estimation ◽

Chi Square ◽

Anderson Darling ◽

The Right

The extreme value theory is expanded by proposing and studying a new version of the Fréchet model. Some new bivariate type extensions using Farlie–Gumbel–Morgenstern copula, modified Farlie–Gumbel–Morgenstern copula, Clayton copula, and Renyi’s entropy copula are derived. After a quick study for its properties, different non-Bayesian estimation methods under uncensored schemes are considered, such as the maximum likelihood estimation method, Anderson–Darling estimation method, ordinary least square estimation method, Cramér–von-Mises estimation method, weighted least square estimation method, left-tail Anderson–Darling estimation method, and right-tail Anderson–Darling estimation method. Numerical simulations were performed for comparing the estimation methods using different sample sizes for three different combinations of parameters. The Barzilai–Borwein algorithm was employed via a simulation study. Three applications were presented for measuring the flexibility and the importance of the new model for comparing the competitive distributions under the uncensored scheme. Using the approach of the Bagdonavicius–Nikulin goodness-of-fit test for validation under the right censored data, we propose a modified chi-square goodness-of-fit test for the new model. The modified goodness-of-fit statistic test was applied for the right censored real data set, called leukemia free-survival times for autologous transplants. Based on the maximum likelihood estimators on initial data, the modified goodness-of-fit test recovered the loss in information while the grouping data and followed chi-square distributions. All elements of the modified goodness-of-fit criteria tests are explicitly derived and given.

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Statistical Examination of Uncaria gambir Roxb Drying Modeling

International Journal of Recent Technology and Engineering - 2 ◽

10.35940/ijrte.b3516.079220 ◽

2020 ◽

Vol 9 (2) ◽

pp. 379-382

Keyword(s):

Root Mean Square Error ◽

Design Process ◽

Goodness Of Fit ◽

Mean Square ◽

Air Velocity ◽

Statistical Parameters ◽

Goodness Of Fit Test ◽

Chi Square ◽

Drying Conditions ◽

Best Fit

This study investigates the drying modeling of Uncaria gambir Roxb using convective desiccant examined by statistical parameters. Three types of drying modeling are investigated, i.e. the Newton, Page and Henderson-Pabis models. The drying conditions of Uncaria gambir Roxb were set at 35oC, 45oC and 55oC and air velocity of 1.2 m/s. The results show that the Page modeling is the best fit model for this investigation based on values of R2 (coefficient of determinant), RMSE (root mean square error) and χ2 (chi-square) goodness of fit test derived from (MR) moisture ratio equation. The Page modeling shows R2 value nearest to unity and lowest values of RMSE and χ2 are obtained for all given temperatures (35oC, 45oC and 55oC) at air velocity of 1.2 m/s. The drying modeling is useful for optimization in design process encountered with product quality and cost of production.

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Fitting The Statistical Distributions To The Daily Rainfall Amount In Peninsular Malaysia

Jurnal Teknologi ◽

10.11113/jt.v46.287 ◽

2012 ◽

Cited By ~ 2

Author(s):

Suhaila Jamaludin ◽

Abdul Aziz Jemain

Keyword(s):

Goodness Of Fit ◽

Daily Rainfall ◽

Peninsular Malaysia ◽

Rainfall Amount ◽

Likelihood Method ◽

Goodness Of Fit Test ◽

Kolmogorov Smirnov ◽

Anderson Darling ◽

Von Mises ◽

Cramer Von Mises

Data hujan harian dibahagikan kepada empat jenis rentetan hujan (jenis 1, 2, 3 dan 4). Taburan Gamma, Weibull, Kappa dan Gabungan Eksponen ialah empat taburan statistik yang diuji dalam memadankan data jumlah hujan harian di Semenanjung Malaysia. Parameter bagi setiap taburan dianggar dengan menggunakan kaedah kebolehjadian maksimum. Model dipilih berdasarkan nilai ralat yang minimum terhasil dari tujuh ujian kesesuaian model iaitu median bagi perbezaan nilai mutlak antara taburan empirik dengan taburan yang diuji, statistik fungsi empirik iaitu Kolmogorov-Smirnov D, Anderson Darling A2 dan Cramer-von-Mises W2 serta kaedah baru statistik fungsi empirik yang berasaskan kepada ujian nisbah kebolehjadian. Berdasarkan nilai ujian kesesuaian model, didapati taburan Gabungan Eksponen adalah yang paling sesuai dalam memadankan data jumlah hujan harian di Semenanjung Malaysia. Kata kunci: Jumlah hujan harian, ujian kesesuaian model, gabungan eksponen Daily rainfall data have been classified according to four rain types of sequence of wet days (Type 1, 2, 3 and 4). The Gamma, Weibull, Kappa and Mixed Exponential are the four distributions that have been tested to fit daily rainfall amount in Peninsular Malaysia. Parameter for each distribution were estimated using the maximum likelihood method. The selected model is chosen based on the minimum error produced by seven goodness-of-fit (GOF) tests namely the medium of absolute difference (MAD) between the empirical and hypothesized distributions, the traditional Empirical Distribution Function (EDF) Statistics which include Kolmogorov-Smirnov statistic D, Anderson Darling statistic A2 and Cramer-von-Mises statistic W2 and the new method of EDF Statistic based on likelihood ratio statistic. Based on these goodness-of-fit test, the Mixed Exponential is found to be the most approriate distribution for describing the daily rainfall amount in Peninsular Malaysia. Key words: Dairy rainfall amount, goodness–of–fit test, mixed exponential

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Examine generalized lambda distribution fitting performance: An application to extreme share return in Malaysia

Malaysian Journal of Fundamental and Applied Sciences ◽

10.11113/mjfas.v13n3.599 ◽

2017 ◽

Vol 13 (3) ◽

Author(s):

Muhammad Fadhil Marsani ◽

Ani Shabri ◽

Nur Amalina Mat Jan

Keyword(s):

Goodness Of Fit ◽

Composite Index ◽

Value Theory ◽

Extreme Value ◽

Correct Prediction ◽

Distribution Fitting ◽

Goodness Of Fit Test ◽

Generalized Lambda Distribution ◽

Index Stock ◽

Anderson Darling

Understand the extreme volatility in the market is important for the investor to make a correct prediction. This paper evaluated the performance of generalized lambda distribution (GLD) by comparing with the popular probability distribution namely generalized extreme value (GEV), Generalized logistic (GLO), generalized Pareto (GPA), and Pearson (PE3) using Kuala Lumpur composite index stock return data. The parameter for each distribution estimated using the L-moment method. Based on k-sample Anderson darling goodness of fit test, GLD performs well in weekly maximum and minimum period. Evidence for preferring GLD as an alternative to extreme value theory distribution also described.

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Prediction of Haemoglobin Level by Some Probability Distribution

Journal of Balkumari College ◽

10.3126/jbkc.v9i1.30090 ◽

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.

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