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 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>

THE COMPARATIVE STUDY OF FUNCTIONAL RESPONSES: EXPERIMENTAL DESIGN AND STATISTICAL INTERPRETATION

1985 ◽  
Vol 117 (5) ◽  
pp. 617-629 ◽  
Author(s):  
Marilyn A. Houck ◽  
Richard E. Strauss
Keyword(s):  
Experimental Design ◽  
Functional Response ◽  
Maximum Likelihood Method ◽  
Graphical Method ◽  
Predation Rate ◽  
Likelihood Method ◽  
Statistical Interpretation ◽  
Functional Responses ◽  
Response Curves ◽  
The Comparative Study

AbstractMathematical discussions of models of functional response (predation rate as a function of prey density) have usually emphasized description of the shape of the functional-response curve. However, lack of congruence between experimental design and data analysis and under-utilization of appropriate statistical methods of analysis have hindered an empirical synthetic treatment of such feeding behavior. Here we review existing experimental and statistical procedures with reference to Holling's generalized model of functional response, and describe: (1) an experimental design compatible with the assumptions of the model; (2) a maximum-likelihood method for fitting the model; (3) several methods for statistical comparison of sets of functional-response curves; and (4) an exploratory graphical method for examining patterns of variation among larger numbers of samples.

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 Measuring Subclusters in Galaxy Clusters

1999 ◽  
Vol 186 ◽  
pp. 417-417
Author(s):  
Z.Y. Shao
Keyword(s):  
Maximum Likelihood ◽  
Radial Velocity ◽  
Galaxy Clusters ◽  
Maximum Likelihood Method ◽  
Velocity Space ◽  
Likelihood Method ◽  
Cluster Region ◽  
Distribution Parameters ◽  
Celestial Sphere ◽  
Image Position

We assume that there are Kc subclusters and Kf fields (foreground or background) in a cluster region. Then, the distribution of all galaxies in this region can be described as follow: where, nc and nf are normalized numbers of subcluster members and field galaxies. φc, φf, are their normalized distributions in radial velocity space. Both of them can be assumed as Gaussian. μc and μf are normalized distributions in the projected surface of the celestial sphere. For field galaxies, it's uniform, and for subcluster members, usually we use the King's approximate formulae. Distribution parameters and their uncertainties can be found by using the standard maximum likelihood method. And membership probabilities of the ith galaxy belonging to the cth subcluster can be calculated as Pc(i) = φc(i)/φp(i).

scholarly journals A maximum likelihood method for estimating genome length using genetic linkage data.

Genetics ◽  
1991 ◽  
Vol 128 (1) ◽  
pp. 175-182 ◽  
Author(s):  
A Chakravarti ◽  
L K Lasher ◽  
J E Reefer
Keyword(s):  
Maximum Likelihood ◽  
Method Of Moments ◽  
Maximum Likelihood Method ◽  
Marker Locus ◽  
Likelihood Method ◽  
Linkage Data ◽  
A Genome ◽  
Marker Loci ◽  
Genetic Length ◽  
Method Of Moments Estimator

Abstract The genetic length of a genome, in units of Morgans or centimorgans, is a fundamental characteristic of an organism. We propose a maximum likelihood method for estimating this quantity from counts of recombinants and nonrecombinants between marker locus pairs studied from a backcross linkage experiment, assuming no interference and equal chromosome lengths. This method allows the calculation of the standard deviation of the estimate and a confidence interval containing the estimate. Computer simulations have been performed to evaluate and compare the accuracy of the maximum likelihood method and a previously suggested method-of-moments estimator. Specifically, we have investigated the effects of the number of meioses, the number of marker loci, and variation in the genetic lengths of individual chromosomes on the estimate. The effect of missing data, obtained when the results of two separate linkage studies with a fraction of marker loci in common are pooled, is also investigated. The maximum likelihood estimator, in contrast to the method-of-moments estimator, is relatively insensitive to violation of the assumptions made during analysis and is the method of choice. The various methods are compared by application to partial linkage data from Xiphophorus.

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