scholarly journals Transformation of circular random variables based on circular distribution functions

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 5931-5947
Author(s):  
Hatami Mojtaba ◽  
Alamatsaz Hossein
Keyword(s):  
Distribution Function ◽  
Random Variables ◽  
Real Data ◽  
Random Variable ◽  
Distribution Functions ◽  
Likelihood Method ◽  
Circular Distribution ◽  
Data Set ◽  
Trigonometric Moments ◽  
Von Mises

In this paper, we propose a new transformation of circular random variables based on circular distribution functions, which we shall call inverse distribution function (id f ) transformation. We show that M?bius transformation is a special case of our id f transformation. Very general results are provided for the properties of the proposed family of id f transformations, including their trigonometric moments, maximum entropy, random variate generation, finite mixture and modality properties. In particular, we shall focus our attention on a subfamily of the general family when id f transformation is based on the cardioid circular distribution function. Modality and shape properties are investigated for this subfamily. In addition, we obtain further statistical properties for the resulting distribution by applying the id f transformation to a random variable following a von Mises distribution. In fact, we shall introduce the Cardioid-von Mises (CvM) distribution and estimate its parameters by the maximum likelihood method. Finally, an application of CvM family and its inferential methods are illustrated using a real data set containing times of gun crimes in Pittsburgh, Pennsylvania.

scholarly journals New Lindley Half Cauchy Distribution: Theory and Applications

2020 ◽  
Vol 9 (4) ◽  
pp. 1-7
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Cauchy Distribution ◽  
Least Square ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Model Parameters ◽  
Data Set ◽  
Von Mises

In this paper, we have defined a new two-parameter new Lindley half Cauchy (NLHC) distribution using Lindley-G family of distribution which accommodates increasing, decreasing and a variety of monotone failure rates. The statistical properties of the proposed distribution such as probability density function, cumulative distribution function, quantile, the measure of skewness and kurtosis are presented. We have briefly described the three well-known estimation methods namely maximum likelihood estimators (MLE), least-square (LSE) and Cramer-Von-Mises (CVM) methods. All the computations are performed in R software. By using the maximum likelihood method, we have constructed the asymptotic confidence interval for the model parameters. We verify empirically the potentiality of the new distribution in modeling a real data set.

scholarly journals Stochastic Comparisons of Some Distances between Random Variables

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 981
Author(s):  
Patricia Ortega-Jiménez ◽  
Miguel A. Sordo ◽  
Alfonso Suárez-Llorens
Keyword(s):  
Financial Risk ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Stochastic Ordering ◽  
Random Variable ◽  
Distribution Functions ◽  
Stochastic Comparisons ◽  
Stochastic Orderings ◽  
Absolute Value ◽  
The Difference

The aim of this paper is twofold. First, we show that the expectation of the absolute value of the difference between two copies, not necessarily independent, of a random variable is a measure of its variability in the sense of Bickel and Lehmann (1979). Moreover, if the two copies are negatively dependent through stochastic ordering, this measure is subadditive. The second purpose of this paper is to provide sufficient conditions for comparing several distances between pairs of random variables (with possibly different distribution functions) in terms of various stochastic orderings. Applications in actuarial and financial risk management are given.

The central limit problem for trimmed sums

1987 ◽  
Vol 102 (2) ◽  
pp. 329-349 ◽  
Author(s):  
Philip S. Griffin ◽  
William E. Pruitt
Keyword(s):  
Distribution Function ◽  
Random Variables ◽  
Random Variable ◽  
Limit Problem ◽  
Absolute Value ◽  
Trimmed Sums ◽  
Common Distribution ◽  
Common Distribution Function ◽  
Central Limit Problem ◽  
Trimmed Sum

Let X, X1, X2,… be a sequence of non-degenerate i.i.d. random variables with common distribution function F. For 1 ≤ j ≤ n, let mn(j) be the number of Xi satisfying either |Xi| > |Xj|, 1 ≤ i ≤ n, or |Xi| = |Xj|, 1 ≤ i ≤ j, and let (r)Xn = Xj if mn(j) = r. Thus (r)Xn is the rth largest random variable in absolute value from amongst X1, …, Xn with ties being broken according to the order in which the random variables occur. Set (r)Sn = (r+1)Xn + … + (n)Xn and write Sn for (0)Sn. We will refer to (r)Sn as a trimmed sum.

scholarly journals Mixture of Inverse Weibull and Lognormal Distributions: Properties, Estimation, and Illustration

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
K. S. Sultan ◽  
A. S. Al-Moisheer
Keyword(s):  
Information Matrix ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Component Mixture ◽  
Data Set ◽  
Hazard Functions ◽  
Lognormal Distributions ◽  
Proposed Model ◽  
Estimation Of Model Parameters

We discuss the two-component mixture of the inverse Weibull and lognormal distributions (MIWLND) as a lifetime model. First, we discuss the properties of the proposed model including the reliability and hazard functions. Next, we discuss the estimation of model parameters by using the maximum likelihood method (MLEs). We also derive expressions for the elements of the Fisher information matrix. Next, we demonstrate the usefulness of the proposed model by fitting it to a real data set. Finally, we draw some concluding remarks.

scholarly journals On Distribution Characteristics of a Fuzzy Random Variable

2018 ◽  
Vol 47 (2) ◽  
pp. 53-67 ◽  
Author(s):  
Jalal Chachi
Keyword(s):  
Probability Theory ◽  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Random Variables ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Distribution Characteristics ◽  
Fuzzy Random Variables ◽  
Fuzzy Random

In this paper, rst a new notion of fuzzy random variables is introduced. Then, usingclassical techniques in Probability Theory, some aspects and results associated to a randomvariable (including expectation, variance, covariance, correlation coecient, etc.) will beextended to this new environment. Furthermore, within this framework, we can use thetools of general Probability Theory to dene fuzzy cumulative distribution function of afuzzy random variable.

A New-Flexible Generated Family of Distributions Based on Half-Logistic Distribution

2020 ◽  
Vol 17 (11) ◽  
pp. 4813-4818
Author(s):  
Sanaa Al-Marzouki ◽  
Sharifah Alrajhi
Keyword(s):  
Logistic Model ◽  
Real Data ◽  
Likelihood Method ◽  
Logistic Distribution ◽  
Data Set ◽  
New Family ◽  
Probability Weighted Moment ◽  
The Subject ◽  
Generated Family ◽  
Family Of Distributions

We proposed a new family of distributions from a half logistic model called the generalized odd half logistic family. We expressed its density function as a linear combination of exponentiated densities. We calculate some statistical properties as the moments, probability weighted moment, quantile and order statistics. Two new special models are mentioned. We study the estimation of the parameters for the odd generalized half logistic exponential and the odd generalized half logistic Rayleigh models by using maximum likelihood method. One real data set is assesed to illustrate the usefulness of the subject family.

scholarly journals Extended Odd Fréchet-G Family of Distributions

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Suleman Nasiru
Keyword(s):  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Data Sets ◽  
Data Set ◽  
New Class ◽  
New Family ◽  
Rate Functions ◽  
The Given ◽  
Family Of Distributions

The need to develop generalizations of existing statistical distributions to make them more flexible in modeling real data sets is vital in parametric statistical modeling and inference. Thus, this study develops a new class of distributions called the extended odd Fréchet family of distributions for modifying existing standard distributions. Two special models named the extended odd Fréchet Nadarajah-Haghighi and extended odd Fréchet Weibull distributions are proposed using the developed family. The densities and the hazard rate functions of the two special distributions exhibit different kinds of monotonic and nonmonotonic shapes. The maximum likelihood method is used to develop estimators for the parameters of the new class of distributions. The application of the special distributions is illustrated by means of a real data set. The results revealed that the special distributions developed from the new family can provide reasonable parametric fit to the given data set compared to other existing distributions.

scholarly journals The Generalized Additive Weibull-G Family of Distributions

2017 ◽  
Vol 6 (5) ◽  
pp. 65 ◽  
Author(s):  
Amal S. Hassan ◽  
Saeed E. Hemeda ◽  
Sudhansu S. Maiti ◽  
Sukanta Pramanik
Keyword(s):  
Maximum Likelihood Method ◽  
Real Data ◽  
Random Variable ◽  
Likelihood Method ◽  
Parameter Estimates ◽  
Data Sets ◽  
New Family ◽  
The Family ◽  
Generated Family ◽  
Family Of Distributions

In this paper, we present a new family, depending on additive Weibull random variable as a generator, called the generalized additive Weibull generated-family (GAW-G) of distributions with two extra parameters. The proposed family involves several of the most famous classical distributions as well as the new generalized Weibull-G family which already accomplished by Cordeiro et al. (2015). Four special models are displayed. The expressions for the incomplete and ordinary moments, quantile, order statistics, mean deviations, Lorenz and Benferroni curves are derived. Maximum likelihood method of estimation is employed to obtain the parameter estimates of the family. The simulation study of the new models is conducted. The efficiency and importance of the new generated family is examined through real data sets.

scholarly journals The Fréchet transform

1993 ◽  
Vol 16 (1) ◽  
pp. 155-164
Author(s):  
Piotor Mikusiński ◽  
Morgan Phillips ◽  
Howard Sherwood ◽  
Michael D. Taylor
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Probability Measure ◽  
Probability Distribution Function ◽  
Random Variables ◽  
Distribution Functions ◽  
Probability Distribution Functions

LetF1,…,FNbe1-dimensional probability distribution functions andCbe anN-copula. Define anN-dimensional probability distribution functionGbyG(x1,…,xN)=C(F1(x1),…,FN(xN)). Letν, be the probability measure induced onℝNbyGandμbe the probability measure induced on[0,1]NbyC. We construct a certain transformationΦof subsets ofℝNto subsets of[0,1]Nwhich we call the Fréchet transform and prove that it is measure-preserving. It is intended that this transform be used as a tool to study the types of dependence which can exist between pairs orN-tuples of random variables, but no applications are presented in this paper.

Smallest-fit selection of random sizes under a sum constraint: weak convergence and moment comparisons

1999 ◽  
Vol 31 (1) ◽  
pp. 178-198 ◽  
Author(s):  
Frans A. Boshuizen ◽  
Robert P. Kertz
Keyword(s):  
Distribution Function ◽  
Point Processes ◽  
Continuous Mapping ◽  
Random Variables ◽  
Random Measure ◽  
Renewal Theory ◽  
Random Variable ◽  
Brownian Bridges ◽  
On Line ◽  
Image Position

In this paper, in work strongly related with that of Coffman et al. [5], Bruss and Robertson [2], and Rhee and Talagrand [15], we focus our interest on an asymptotic distributional comparison between numbers of ‘smallest’ i.i.d. random variables selected by either on-line or off-line policies. Let X1,X2,… be a sequence of i.i.d. random variables with distribution function F(x), and let X1,n,…,Xn,n be the sequence of order statistics of X1,…,Xn. For a sequence (cn)n≥1 of positive constants, the smallest fit off-line counting random variable is defined by Ne(cn) := max {j ≤ n : X1,n + … + Xj,n ≤ cn}. The asymptotic joint distributional comparison is given between the off-line count Ne(cn) and on-line counts Nnτ for ‘good’ sequential (on-line) policies τ satisfying the sum constraint ∑j≥1XτjI(τj≤n) ≤ cn. Specifically, for such policies τ, under appropriate conditions on the distribution function F(x) and the constants (cn)n≥1, we find sequences of positive constants (Bn)n≥1, (Δn)n≥1 and (Δ'n)n≥1 such that for some non-degenerate random variables W and W'. The major tools used in the paper are convergence of point processes to Poisson random measure and continuous mapping theorems, strong approximation results of the normalized empirical process by Brownian bridges, and some renewal theory.

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