A New Class of Integrals Involving Extended Mittag–Leffler Functions

In the present work, we evaluate a unified Eulerian type integral whose integrand involves the product of a polynomial system and the multivariable H-function having general arguments. Our integral formula encompasses a very large number of integrals and provides interesting unifieation and extensions of several known (e.g., [1], [3], [4], [5], [9], [11], etc.) and new results. Since the integral has been given in a compact form free from infinite series, it is likely to prove useful in applications. Three special cases of the main integral (which are also sufficiently general in nature and are of interest in themselves) have also been given. Finally, the main integral formula has been expressed as a fractional integral operator to make it more useful in applications.

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Survival and Reliability Analysis with an Epsilon-Positive Family of Distributions with Applications

Symmetry ◽

10.3390/sym13050908 ◽

2021 ◽

Vol 13 (5) ◽

pp. 908

Author(s):

Perla Celis ◽

Rolando de la Cruz ◽

Claudio Fuentes ◽

Héctor W. Gómez

Keyword(s):

Survival Data ◽

Maximum Likelihood Estimates ◽

New Class ◽

New Family ◽

Gamma Distributions ◽

Special Cases ◽

Log Normal ◽

Positive Support ◽

Positive Distributions ◽

Family Of Distributions

We introduce a new class of distributions called the epsilon–positive family, which can be viewed as generalization of the distributions with positive support. The construction of the epsilon–positive family is motivated by the ideas behind the generation of skew distributions using symmetric kernels. This new class of distributions has as special cases the exponential, Weibull, log–normal, log–logistic and gamma distributions, and it provides an alternative for analyzing reliability and survival data. An interesting feature of the epsilon–positive family is that it can viewed as a finite scale mixture of positive distributions, facilitating the derivation and implementation of EM–type algorithms to obtain maximum likelihood estimates (MLE) with (un)censored data. We illustrate the flexibility of this family to analyze censored and uncensored data using two real examples. One of them was previously discussed in the literature; the second one consists of a new application to model recidivism data of a group of inmates released from the Chilean prisons during 2007. The results show that this new family of distributions has a better performance fitting the data than some common alternatives such as the exponential distribution.

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A New Class of Estimators Based on a General Relative Loss Function

Mathematics ◽

10.3390/math9101138 ◽

2021 ◽

Vol 9 (10) ◽

pp. 1138

Author(s):

Tao Hu ◽

Baosheng Liang

Keyword(s):

Loss Function ◽

Asymptotically Normal ◽

New Class ◽

Statistical Inferences ◽

Relative Loss ◽

Special Cases ◽

Class Of Estimators ◽

Box Cox Transformation ◽

Loss Estimator ◽

Prostate Cancer Study

Motivated by the relative loss estimator of the median, we propose a new class of estimators for linear quantile models using a general relative loss function defined by the Box–Cox transformation function. The proposed method is very flexible. It includes a traditional quantile regression and median regression under the relative loss as special cases. Compared to the traditional linear quantile estimator, the proposed estimator has smaller variance and hence is more efficient in making statistical inferences. We show that, in theory, the proposed estimator is consistent and asymptotically normal under appropriate conditions. Extensive simulation studies were conducted, demonstrating good performance of the proposed method. An application of the proposed method in a prostate cancer study is provided.

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Certain Unified Integrals Involving a Multivariate Mittag–Leffler Function

Axioms ◽

10.3390/axioms10020081 ◽

2021 ◽

Vol 10 (2) ◽

pp. 81

Author(s):

Shilpi Jain ◽

Ravi P. Agarwal ◽

Praveen Agarwal ◽

Prakash Singh

Keyword(s):

Integral Formulas ◽

Special Cases

A remarkably large number of unified integrals involving the Mittag–Leffler function have been presented. Here, with the same technique as Choi and Agarwal, we propose the establishment of two generalized integral formulas involving a multivariate generalized Mittag–Leffler function, which are expressed in terms of the generalized Lauricella series due to Srivastava and Daoust. We also present some interesting special cases.

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Mixed quasi invex equilibrium problems

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171204310112 ◽

2004 ◽

Vol 2004 (57) ◽

pp. 3057-3067 ◽

Cited By ~ 4

Author(s):

Muhammad Aslam Noor

Keyword(s):

Variational Inequalities ◽

Equilibrium Problems ◽

Strong Monotonicity ◽

Auxiliary Principle ◽

Auxiliary Principle Technique ◽

Iterative Schemes ◽

New Class ◽

Special Cases ◽

Weaker Conditions

We introduce a new class of equilibrium problems, known asmixed quasi invex equilibrium(orequilibrium-like) problems. This class of invex equilibrium problems includes equilibrium problems, variational inequalities, and variational-like inequalities as special cases. Several iterative schemes for solving invex equilibrium problems are suggested and analyzed using the auxiliary principle technique. It is shown that the convergence of these iterative schemes requires either pseudomonotonicity or partially relaxed strong monotonicity, which are weaker conditions than the previous ones. As special cases, we also obtained the correct forms of the algorithms for solving variational-like inequalities, which have been considered in the setting of convexity. In fact, our results represent significant and important refinements of the previously known results.

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Multivariate fractional phase–type distributions

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2020-0071 ◽

2020 ◽

Vol 23 (5) ◽

pp. 1431-1451 ◽

Cited By ~ 1

Author(s):

Hansjörg Albrecher ◽

Martin Bladt ◽

Mogens Bladt

Keyword(s):

Tail Dependence ◽

Jump Process ◽

Multivariate Distributions ◽

New Class ◽

Natural Time ◽

Special Cases ◽

Phase Type ◽

Phase Type Distributions ◽

Markovian Jump Process ◽

Heavy Tailed

Abstract We extend the Kulkarni class of multivariate phase–type distributions in a natural time–fractional way to construct a new class of multivariate distributions with heavy-tailed Mittag-Leffler(ML)-distributed marginals. The approach relies on assigning rewards to a non–Markovian jump process with ML sojourn times. This new class complements an earlier multivariate ML construction [2] and in contrast to the former also allows for tail dependence. We derive properties and characterizations of this class, and work out some special cases that lead to explicit density representations.

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Univariate and bivariate extensions of the generalized exponential distributions

Mathematica Slovaca ◽

10.1515/ms-2021-0073 ◽

2021 ◽

Vol 71 (6) ◽

pp. 1581-1598

Author(s):

Vahid Nekoukhou ◽

Ashkan Khalifeh ◽

Hamid Bidram

Keyword(s):

Em Algorithm ◽

Exponential Distribution ◽

Bivariate Distribution ◽

Generalized Exponential Distribution ◽

Exponential Distributions ◽

Unknown Parameters ◽

Data Set ◽

New Class ◽

Special Cases ◽

Univariate Distribution

Abstract The main aim of this paper is to introduce a new class of continuous generalized exponential distributions, both for the univariate and bivariate cases. This new class of distributions contains some newly developed distributions as special cases, such as the univariate and also bivariate geometric generalized exponential distribution and the exponential-discrete generalized exponential distribution. Several properties of the proposed univariate and bivariate distributions, and their physical interpretations, are investigated. The univariate distribution has four parameters, whereas the bivariate distribution has five parameters. We propose to use an EM algorithm to estimate the unknown parameters. According to extensive simulation studies, we see that the effectiveness of the proposed algorithm, and the performance is quite satisfactory. A bivariate data set is analyzed and it is observed that the proposed models and the EM algorithm work quite well in practice.

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Damping Characteristics of a Cantilever Plate Using Permanent Magnetic Constrained Layer Damping Strip Treatment

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.450-451.466 ◽

2012 ◽

Vol 450-451 ◽

pp. 466-471

Author(s):

Ming Li ◽

Hui Ming Zheng

Keyword(s):

Ritz Method ◽

Constrained Layer Damping ◽

Structural Vibrations ◽

Torsional Mode ◽

Calculation Of Parameters ◽

New Class ◽

Damping Characteristics ◽

Special Cases ◽

Cantilever Rectangular Plate ◽

Passive Constrained Layer Damping

Significant improvement of damping characteristics can be achieved by using the new class of magnetic constrained layer damping treatment (MCLD). This paper presents the damping properties of the first and second torsional mode for a five-layer cantilever rectangular plate treated with partial MCLD. The Rayleigh-Ritz method and Hamilton’s principle are employed in the analysis. We have chosen both single and segmented patches with different sizes. It can be observed that for the two modes single-patched MCLD treatment induces less improvement of damping characteristics especially for the short patch. The effects of calculation of parameters like placement strategies of discrete patches, the length of patches are analyzed and discussed. The results obtained from analytical show that the optimum location of the patch, for the torsional mode, is at edge of the plate. Favorable comparisons with the conventional passive constrained layer damping treatment (PCLD) on various special cases of the problem are obtained. The results demonstrate MCLD treatment still improvements over PCLD in damping structural vibrations.

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Pathway fractional integral operators of generalized k-wright function and k4-function

Boletim da Sociedade Paranaense de Matemática ◽

10.5269/bspm.v35i2.29180 ◽

2017 ◽

Vol 35 (2) ◽

pp. 235 ◽

Cited By ~ 2

Author(s):

Dinesh Kumar ◽

Ram Kishore Saxena ◽

Jitendra Daiya

Keyword(s):

Fractional Integral ◽

Fractional Integration ◽

Integral Operators ◽

Wright Function ◽

Finite Product ◽

Fractional Integral Operators ◽

Integral Formulas ◽

Fractional Integration Operator ◽

Composition Formula ◽

Special Cases

In the present work we introduce a composition formula of the pathway fractional integration operator with finite product of generalized K-Wright function and K4-function. The obtained results are in terms of generalized Wright function.Certain special cases of the main results given here are also considered to correspond with some known and new (presumably) pathway fractional integral formulas.

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Some remarks on functions with values in probabilistic normed spaces

Mathematica Slovaca ◽

10.2478/s12175-007-0021-8 ◽

2007 ◽

Vol 57 (3) ◽

Cited By ~ 7

Author(s):

Ioan Goleţ

Keyword(s):

Normed Space ◽

Topological Properties ◽

Normed Spaces ◽

Probabilistic Normed Space ◽

Random Functions ◽

New Class ◽

Probabilistic Normed Spaces ◽

Special Cases ◽

Probabilistic Norm

AbstractIn this paper we consider an enlargement of the notion of the probabilistic normed space. For this new class of probabilistic normed spaces we give some topological properties. By using properties of the probabilistic norm we prove some differential and integral properties of functions with values into probabilistic normed spaces. As special cases, results for deterministic and random functions can be obtained.

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