scholarly journals A Skewed Truncated Cauchy Uniform Distribution and Its Moments

2016 ◽  
Vol 10 (7) ◽  
pp. 174
Author(s):  
Zahra Nazemi Ashani ◽  
Mohd Rizam Abu Bakar ◽  
Noor Akma Ibrahim ◽  
Mohd Bakri Adam.
Keyword(s):  
Distribution Function ◽  
Normal Distribution ◽  
Uniform Distribution ◽  
Probability Distribution Function ◽  
Maximum Likelihood Method ◽  
Cauchy Distribution ◽  
Likelihood Method ◽  
Symmetric Distributions ◽  
Finite Moments ◽  
Skewness And Kurtosis

<p>Although usually normal distribution is considered for statistical analysis, however in many practical situations, distribution of data is asymmetric and using the normal distribution is not appropriate for modeling the data. Base on this fact, skew symmetric distributions have been introduced. In this article, between skew distributions, we consider the skew Cauchy symmetric distributions because this family of distributions doesn't have finite moments of all orders. We focus on skew Cauchy uniform distribution and generate the skew probability distribution function of the form , where  is truncated Cauchy distribution and  is the distribution function of uniform distribution. The finite moments of all orders and distribution function for this new density function are provided. At the end, we illustrate this model using exchange rate data and show, according to the maximum likelihood method, this model is a better model than skew Cauchy distribution. Also the range of skewness and kurtosis for  and the graphical illustrations are provided.</p>

scholarly journals Lomax Weibull Distribution

2019 ◽  
pp. 1-18 ◽  
Author(s):  
Benjamin Apam ◽  
Nasiru Suleman ◽  
Emmanuel Adjei
Keyword(s):  
Distribution Function ◽  
Maximum Likelihood ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Maximum Likelihood Method ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Survival Functions ◽  
Score Functions ◽  
The Moment

In this article, we introduce the Lomax-Weibull (LoW) distribution using the method of composition of CDFs from the Lomax and Weibull distributions. Expressions for the moment generating function, hazard and survival functions were derived. A plot of the probability distribution function and cumulative distributions were done using the Python software. We also used the maximum likelihood method of estimation to derive the score functions for estimating the parameters of the distribution.

Statistical evaluation of fatigue tests using maximum likelihood

2021 ◽  
Vol 63 (8) ◽  
pp. 714-720
Author(s):  
Klaus Störzel ◽  
Jörg Baumgartner
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Test Data ◽  
Maximum Likelihood Method ◽  
Statistical Evaluation ◽  
Test Procedure ◽  
Fatigue Tests ◽  
Likelihood Method ◽  
Parameter Determination ◽  
Number Of Cycles

Abstract The statistical evaluation of fatigue tests can be carried out using the maximum likelihood method. With this method, the influence of run-outs on the S-N curve can be statistically considered. Typically, a bilinear S-N curve (Wöhler curve) in double-logarithmic representation is used. The logarithmic normal distribution is the basis for describing the scatter, which is assumed here to be independent of the number of cycles. For parameter determination via the maximum likelihood method, reliability is examined and compared with the evaluation methods proposed in DIN 50100. While a defined test procedure is required for the application of DIN 50100, any test data can be evaluated according to the maximum likelihood method. In comparison with the methods proposed in DIN 50100, it could be shown through some examples that the maximum likelihood method yields very reliable results for all S-N curve parameters.

Optimization of Parameters Estimation for Normal Distribution Based on Bootstrap Method

2011 ◽  
Vol 52-54 ◽  
pp. 546-549
Author(s):  
Shi Bo Xin
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Maximum Likelihood Method ◽  
Simulation Analysis ◽  
Bootstrap Method ◽  
Parameters Estimation ◽  
Likelihood Method ◽  
Sample Mean ◽  
Optimization Of Parameters

According to sample mean submits normal distribution which is extracted from normal distribution, we give the equation of parameters estimation for normal distribution by bootstrap method, then we make a simulation analysis and compare the effect of parameters estimation which uses traditional maximum likelihood method and bootstrap method.

scholarly journals Rainfall models – a study over Gangtok

MAUSAM ◽  
2021 ◽  
Vol 61 (2) ◽  
pp. 225-228
Author(s):  
K. SEETHARAM
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Uniform Distribution ◽  
Probability Distribution Function ◽  
Null Hypothesis ◽  
Probability Distributions ◽  
Data Sets ◽  
Type I ◽  
Anderson Darling ◽  
Pearsonian Type

In this paper, the Pearsonian system of curves were fitted to the monthly rainfalls from January to December, in addition to the seasonal as well as annual rainfalls totalling to 14 data sets of the period 1957-2005 with 49 years of duration for the station Gangtok to determine the probability distribution function of these data sets. The study indicated that the monthly rainfall of July and summer monsoon seasonal rainfall did not fit in to any of the Pearsonian system of curves, but the monthly rainfalls of other months and the annual rainfalls of Gangtok station indicated to fit into Pearsonian type-I distribution which in other words is an uniform distribution. Anderson-Darling test was applied to for null hypothesis. The test indicated the acceptance of null-hypothesis. The statistics of the data sets and their probability distributions are discussed in this paper.

scholarly journals A New Approach to Assess Wind Potential

2021 ◽  
Keyword(s):  
Distribution Function ◽  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Wind Power ◽  
Cumulative Distribution Function ◽  
Maximum Likelihood Method ◽  
New Method ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Wind Distribution

<p>Weibull Cumulative Distribution Function (C.D.F.) has been employed to assess and compare wind potentials of two wind stations Europlatform and Stavenisse of The Netherland. Weibull distribution has been used for accurate estimation of wind energy potential for a long time. The Weibull distribution with two parameters is suitable for modeling wind data if wind distribution is unimodal. Whereas wind distribution is generally unimodal, random weather changes can make the distribution bimodal. It is always desirable to find a method that accurately represents actual statistical data. Some well-known statistical methods are Method of Moment (MoM), Linear Least Square Method (LLSM), Maximum Likelihood Method (M.L.M.), Modified Maximum Likelihood Method (MMLM), Energy Pattern Factor Method (EPFM), and Empirical Method (E.M.), etc. All these methods employ Probability Density Function (PDF) of Weibull distribution, except LLSM, which uses Cumulative Distribution Function (C.D.F.). In this communication, we are presenting a newly proposed method of evaluating Weibull parameters. Unlike most methods, this new method employs a cumulative distribution function. A MATLAB® GUI-based simulation is developed to estimate Weibull parameters using the C.D.F. approach. It is found that the Mean Square Error (M.S.E.) is the lowest when using the new method. The new method, therefore, estimates wind power density with reasonable accuracy. Wind Power (W.P.) is estimated by considering four different Wind Turbine (W.T.) models for two sites, and maximum W.P. is found using Evance R9000.</p>

scholarly journals Multistage Curve Fitting

1977 ◽  
Vol 9 (1-2) ◽  
pp. 191-202 ◽  
Author(s):  
Christoph Haehling von Lanzenauer ◽  
Don Wright
Keyword(s):  
Distribution Function ◽  
Method Of Moments ◽  
Curve Fitting ◽  
Maximum Likelihood Method ◽  
Graphical Method ◽  
Decision Makers ◽  
Third Party ◽  
Likelihood Method ◽  
Bodily Injury ◽  
Image Position

One of the most important properties of a distribution function is that it fits the data well enough for the decision-makers' or analysts' purposes. The statisticians' problem is to select a specific form for the distribution function and to determine its parameters from the available data. Various methods (graphical method, method of moments, maximum likelihood method) are available for that purpose.In many real world situations a single distribution function, however, may not be appropriate over the entire range of the available data. This suggests that the underlying process changes over the range of the respective variable. This fact should be considered in curve fitting. A typical example of such a situation is given in Figure 1 representing third party liability losses for trucks.It is interesting to speculate about the different raisons d'être (Seal [5]) for the observed discontinuity. It may be the result of out-of-court or in-court settlements or could stem from differences between bodily injury and property damages.

scholarly journals An Improved Double-Gaussian Closure for the Subgrid Vertical Velocity Probability Distribution Function

2019 ◽  
Vol 76 (1) ◽  
pp. 285-304 ◽  
Author(s):  
A. C. Fitch
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Vertical Velocity ◽  
Probability Distribution Function ◽  
Cumulus Cloud ◽  
Turbulence Statistics ◽  
Shallow Cumulus ◽  
Velocity Probability ◽  
Non Gaussian ◽  
Skewness And Kurtosis

Abstract The vertical velocity probability distribution function (PDF) is analyzed throughout the depth of the lower atmosphere, including the subcloud and cloud layers, in four large-eddy simulation (LES) cases of shallow cumulus and stratocumulus. Double-Gaussian PDF closures are examined to test their ability to represent a wide range of turbulence statistics, from stratocumulus cloud layers characterized by Gaussian turbulence to shallow cumulus cloud layers displaying strongly non-Gaussian turbulence statistics. While the majority of the model closures are found to perform well in the former case, the latter presents a considerable challenge. A new model closure is suggested that accounts for high skewness and kurtosis seen in shallow cumulus cloud layers. The well-established parabolic relationship between skewness and kurtosis is examined, with results in agreement with previous studies for the subcloud layer. In cumulus cloud layers, however, a modified relationship is necessary to improve performance. The new closure significantly improves the estimation of the vertical velocity PDF for shallow cumulus cloud layers, in addition to performing well for stratocumulus. In particular, the long updraft tail representing the bulk of cloudy points is much better represented and higher-order moments diagnosed from the PDF are also greatly improved. However, some deficiencies remain owing to fundamental limitations of representing highly non-Gaussian turbulence statistics with a double-Gaussian PDF.

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