scholarly journals Probability of rainfall for the city of Cruzeiro do Sul, Acre, Brazil

2021 ◽  
Vol 16 (1) ◽  
pp. 1
Author(s):  
Jefferson Rodrigues dos Santos Silva ◽  
Matheus Kucmanski Taveira ◽  
Rodrigo Otávio Peréa Serrano ◽  
Anderson Azevedo Mesquita ◽  
José Genivaldo do Vale Moreira
Keyword(s):  
Gamma Distribution ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Annual Rainfall ◽  
Distribution Parameters ◽  
Kolmogorov Smirnov ◽  
The Mean ◽  
The City ◽  
Rain Precipitation ◽  
Smirnov Test

Due to randomness in the occurrence of hydrological phenomena, the estimation of probable rain precipitation in a given region is important in assisting decision-making. This work aimed to adjust the probabilistic model of the Gamma distribution to the monthly and annual rainfall totals recorded in the city of Cruzeiro do Sul, Acre, for the period between 1970 and 2019, in addition to estimating the expected values at different probability levels. Using the maximum likelihood method, the distribution parameters were estimated, with adherence ratified by the Kolmogorov-Smirnov test. The results showed that the Gamma distribution was adequate to adjust the data; the region has two well-defined periods in its rainfall pattern; the mean precipitation values recorded in the locality are between 25% and 40% of probability. Finally, probable rainfall values were presented at different probability levels for the city of Cruzeiro do Sul.

scholarly journals Bayesian Inference on the Generalized Gamma Distribution using Conjugate Priors

2020 ◽  
Vol 28 (2) ◽  
Keyword(s):  
Gamma Distribution ◽  
Maximum Likelihood Method ◽  
Loss Functions ◽  
Likelihood Method ◽  
Generalized Gamma Distribution ◽  
Bayesian Techniques ◽  
Conjugate Priors ◽  
Generalized Gamma ◽  
The Mean ◽  
Least Squares Approach

This paper focuses on the three-parameter generalized gamma distribution and uses Bayesian techniques to estimate its parameters. Many authors con-sidered estimating the parameters of the generalized gamma distribution in a Bayesian framework using Jeffrey’s priors. Others used different loss functions and the least squares approach. This study uses Bayesian techniques to estimate the three-parameter generalized gamma distribution by using conjugate priors. The random Metropolis algorithm is used to simulate the Bayesian estimates of the three parameters. Then these estimates are compared to the maximum like-lihood estimates using the mean error through simulation. It has been shown in this paper that the obtained estimates using this approach is more accurate than the traditional methods of estimation such as the Maximum likelihood method. The same approach is then used to estimate the parameters of mixtures of the generalized gamma parameters using conjugate priors.

scholarly journals Transmuted Mukherjee-Islam Distribution: A Generalization of Mukherjee-Islam Distribution

2017 ◽  
Vol 9 (4) ◽  
pp. 135
Author(s):  
Loai M. A. Al-Zou'bi
Keyword(s):  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Continuous Distribution ◽  
Quantile Function ◽  
Descriptive Statistics ◽  
Likelihood Method ◽  
Distribution Parameters ◽  
Rate Functions ◽  
Mean Variance ◽  
New Distribution

A new continuous distribution is proposed in this paper. This distribution is a generalization of Mukherjee-Islam distribution using the quadratic rank transmutation map. It is called transmuted Mukherjee-Islam distribution (TMID). We have studied many properties of the new distribution: Reliability and hazard rate functions. The descriptive statistics: mean, variance, skewness, kurtosis are also studied. Maximum likelihood method is used to estimate the distribution parameters. Order statistics and Renyi and Tsallis entropies were also calculated. Furthermore, the quantile function and the median are calculated.

scholarly journals Erosive rainfall in the Rio do Peixe Valley: Part III - Risk of extreme events

2018 ◽  
Vol 22 (1) ◽  
pp. 63-68
Author(s):  
Álvaro J. Back ◽  
Augusto C. Pola ◽  
Nilzo I. Ladwig ◽  
Hugo Schwalm
Keyword(s):  
Extreme Events ◽  
Annual Rainfall ◽  
Data Series ◽  
Rainfall Erosivity ◽  
Significance Level ◽  
Control Structures ◽  
Kolmogorov Smirnov ◽  
Runoff Control ◽  
The Mean ◽  
Erosive Rainfall

ABSTRACT Understanding the risks of extreme events related to soil erosion is important for adequate dimensioning of erosion and runoff control structures. The objective of this study was to determine the rainfall erosivity with different return periods for the Valley of the Rio do Peixe in Santa Catarina state, Brazil. Daily pluviographic data series from 1984 to 2014 from the Campos Novos, and Videira meteorological stations and from 1986 to 2014 from the Caçador station were used. The data series of maximum annual rainfall intensity in 30 min, maximum annual erosive rainfall, and total annual erosivity were analyzed for each station. The Gumbel-Chow distributions were adjusted and their adhesions were evaluated by the Kolmogorov-Smirnov test at a significance level of 5%. The Gumbel-Chow distribution was adequate for the estimation of all studied variables. The mean annual erosivity corresponds to the return period of 2.25 years. The data series of the annual maximum individual rainfall erosivity coefficients varied from 47 to 50%.

scholarly journals Best estimation for the Reliability of 2-parameter Weibull Distribution

2009 ◽  
Vol 6 (4) ◽  
pp. 705-710
Author(s):  
Baghdad Science Journal
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Mean Square Error ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Statistical Criterion ◽  
Mean Square ◽  
Simulation Process ◽  
The Mean ◽  
Two Parameter

This Research Tries To Investigate The Problem Of Estimating The Reliability Of Two Parameter Weibull Distribution,By Using Maximum Likelihood Method, And White Method. The Comparison Is done Through Simulation Process Depending On Three Choices Of Models (?=0.8 , ß=0.9) , (?=1.2 , ß=1.5) and (?=2.5 , ß=2). And Sample Size n=10 , 70, 150 We Use the Statistical Criterion Based On the Mean Square Error (MSE) For Comparison Amongst The Methods.

The influence of water temperature and pH on the survival of Fasciola hepatica miracidia

Parasitology ◽  
1984 ◽  
Vol 88 (1) ◽  
pp. 97-104 ◽  
Author(s):  
G. Smith ◽  
B. T. Grenfell
Keyword(s):  
Maximum Likelihood Method ◽  
Fasciola Hepatica ◽  
Good Description ◽  
Survival Function ◽  
Experimental Studies ◽  
Likelihood Method ◽  
Confidence Limits ◽  
Mean Values ◽  
Influence Of Water ◽  
The Mean

SUMMARYExperimental studies on the survival of Fasciola hepatica miracidia show no evidence that miracidial mortality varies with the pH of the medium, at least in the range 6·0–8·0. On the other hand, miracidial mortality is shown to vary with both the temperature of the medium and the age of the larvae. The mean expected life-span of the miracidium decreases from about 35 h at 6°C to about 6° h at 25° C. The Gompertz survival function provides a good description of the miracidial survivorship curves over the range of temperatures used, and we describe, a maximum likelihood method of estimating the mean values of the parameters of this function, together with their approximate 95% confidence limits.

Zero-truncated Poisson-Lindley distribution

2021 ◽  
pp. 40-50
Author(s):  
Afida Nurul Hilma ◽  
Dian Lestari ◽  
Sindy Devila
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Lindley Distribution ◽  
Count Distribution ◽  
Distribution Parameters ◽  
Counting Distribution ◽  
Over Dispersion

In order to find a counting distribution that can handle the condition when the data has no zero-count. Distribution named Zero-truncated Poisson-Lindley distribution is developed. It can handle the condition when the data has no zero-count both in over-dispersion and under-dispersion. In this paper, characteristics of Zero-truncated Poisson-Lindley distribution are obtained and estimate distribution parameters using the maximum likelihood method. Then, the application of the model to real data is given.

scholarly journals A Cautionary Note on the Use of the Kolmogorov–Smirnov Test for Normality

2007 ◽  
Vol 135 (3) ◽  
pp. 1151-1157 ◽  
Author(s):  
Dag J. Steinskog ◽  
Dag B. Tjøstheim ◽  
Nils G. Kvamstø
Keyword(s):  
Goodness Of Fit ◽  
Small Sample ◽  
Power Comparison ◽  
Goodness Of Fit Test ◽  
Kolmogorov Smirnov ◽  
The Mean ◽  
Small Sample Problem ◽  
Tests For Normality ◽  
Test For Normality ◽  
Smirnov Test

Abstract The Kolmogorov–Smirnov goodness-of-fit test is used in many applications for testing normality in climate research. This note shows that the test usually leads to systematic and drastic errors. When the mean and the standard deviation are estimated, it is much too conservative in the sense that its p values are strongly biased upward. One may think that this is a small sample problem, but it is not. There is a correction of the Kolmogorov–Smirnov test by Lilliefors, which is in fact sometimes confused with the original Kolmogorov–Smirnov test. Both the Jarque–Bera and the Shapiro–Wilk tests for normality are good alternatives to the Kolmogorov–Smirnov test. A power comparison of eight different tests has been undertaken, favoring the Jarque–Bera and the Shapiro–Wilk tests. The Jarque–Bera and the Kolmogorov–Smirnov tests are also applied to a monthly mean dataset of geopotential height at 500 hPa. The two tests give very different results and illustrate the danger of using the Kolmogorov–Smirnov test.

scholarly journals comparison of methods for the estimation of Weibull distribution parameters

2014 ◽  
Vol 11 (1) ◽  
Author(s):  
Felix Nwobi ◽  
Chukwudi Ugomma
Keyword(s):  
Weibull Distribution ◽  
Stock Prices ◽  
Goodness Of Fit ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Goodness Of Fit Tests ◽  
Distribution Parameters ◽  
Kolmogorov Smirnov ◽  
The Mean ◽  
Maximum Likelihood Estimation Method

In this paper we study the different methods for estimation of the parameters of the Weibull distribution. These methods are compared in terms of their fits using the mean square error (MSE) and the Kolmogorov-Smirnov (KS) criteria to select the best method. Goodness-of-fit tests show that the Weibull distribution is a good fit to the squared returns series of weekly stock prices of Cornerstone Insurance PLC. Results show that the mean rank (MR) is the best method among the methods in the graphical and analytical procedures. Numerical simulation studies carried out show that the maximum likelihood estimation method (MLE) significantly outperformed other methods.

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