Generalized length biased distributions

Giri S. Lingappaiah

Displaying similar documents to “Generalized length biased distributions”

Premium evaluation for different loss distributions using utility theory

Harman Preet Singh Kapoor, Kanchan Jain (2011)

Discussiones Mathematicae Probability and Statistics

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For any insurance contract to be mutually advantageous to the insurer and the insured, premium setting is an important task for an actuary. The maximum premium ( $P_{m a x})$ that an insured is willing to pay can be determined using utility theory. The main focus of this paper is to determine $P_{m a x}$ by considering different forms of the utility function. The loss random variable is assumed to follow different Statistical distributions viz Gamma, Beta, Exponential, Pareto, Weibull, Lognormal and Burr....

Automata, algebraicity and distribution of sequences of powers

Jean-Paul Allouche, Jean-Marc Deshouillers, Teturo Kamae, Tadahiro Koyanagi (2001)

Annales de l’institut Fourier

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Let $K$ be a finite field of characteristic $p$ . Let $K ((x))$ be the field of formal Laurent series $f (x)$ in $x$ with coefficients in $K$ . That is, $f (x) = \sum_{n = n_{0}}^{\infty} f_{n} x^{n}$ with $n_{0} \in 𝐙$ and $f_{n} \in K (n = n_{0}, n_{0} + 1, \dots)$ . We discuss the distribution of ${({f^{m}})}_{m = 0, 1, 2, \dots}$ for $f \in K ((x))$ , where ${f} : = \sum_{n = 0}^{\infty} f_{n} x^{n} \in K [[x]]$ denotes the nonnegative part of $f \in K ((x))$ . This is a little different from the real number case where the fractional part that excludes constant term (digit of order 0) is considered. We give an alternative proof of a result by De Mathan obtaining the generic...

Global approximations for the γ-order Lognormal distribution

Thomas L. Toulias (2013)

Discussiones Mathematicae Probability and Statistics

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A generalized form of the usual Lognormal distribution, denoted with $_{γ}$ , is introduced through the γ-order Normal distribution $_{γ}$ , with its p.d.f. defined into (0,+∞). The study of the c.d.f. of $_{γ}$ is focused on a heuristic method that provides global approximations with two anchor points, at zero and at infinity. Also evaluations are provided while certain bounds are obtained.

Bivariate gamma distribution as a life test model

Giri S. Lingappaiah (1984)

Aplikace matematiky

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The bivariate gamma distribution is taken as a life test model to analyse a series system with two dependent components $x$ and $y$ . First, the distribution of a function of $x$ and $y$ , that is, minimum $(x, y)$ , is obtained. Next, the reliability of the component system is evaluated and tabulated for various values of the parameters. Estimates of the parameters are also obtained by using Bayesian approach. Finally, a table of the mean and variance of minimum $(x, y)$ for various values of the parameters...

Uniformly convex spiral functions and uniformly spirallike functions associated with Pascal distribution series

Gangadharan Murugusundaramoorthy, Basem Aref Frasin, Tariq Al-Hawary (2022)

Mathematica Bohemica

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The aim of this paper is to find the necessary and sufficient conditions and inclusion relations for Pascal distribution series to be in the classes ${𝒮𝒫}_{p} (α, β)$ and ${𝒰𝒞𝒱}_{p} (α, β)$ of uniformly spirallike functions. Further, we consider an integral operator related to Pascal distribution series. Several corollaries and consequences of the main results are also considered.

Characterizations of continuous distributions through inequalities involving the expected values of selected functions

Faranak Goodarzi, Mohammad Amini, Gholam Reza Mohtashami Borzadaran (2017)

Applications of Mathematics

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Nanda (2010) and Bhattacharjee et al. (2013) characterized a few distributions with help of the failure rate, mean residual, log-odds rate and aging intensity functions. In this paper, we generalize their results and characterize some distributions through functions used by them and Glaser’s function. Kundu and Ghosh (2016) obtained similar results using reversed hazard rate, expected inactivity time and reversed aging intensity functions. We also, via $w (\cdot)$ -function defined by Cacoullos...

A characterization of the space $D_{F}^{'}$

S. Pilipović (1982)

Matematički Vesnik

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On asymmetric distributions of copula related random variables which includes the skew-normal ones

Ayyub Sheikhi, Fereshteh Arad, Radko Mesiar (2022)

Kybernetika

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Assuming that $C_{X, Y}$ is the copula function of $X$ and $Y$ with marginal distribution functions $F_{X} (x)$ and $F_{Y} (y)$ , in this work we study the selection distribution $Z \overset{d}{=} (X | Y \in T)$ . We present some special cases of our proposed distribution, among them, skew-normal distribution as well as normal distribution. Some properties such as moments and moment generating function are investigated. Also, some numerical analysis is presented for illustration.

The right tail exponent of the Tracy–Widom $β$ distribution

Laure Dumaz, Bálint Virág (2013)

Annales de l'I.H.P. Probabilités et statistiques

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The Tracy–Widom $β$ distribution is the large dimensional limit of the top eigenvalue of $β$ random matrix ensembles. We use the stochastic Airy operator representation to show that as $a \to \infty$ the tail of the Tracy–Widom distribution satisfies $P ({𝑇𝑊}_{β} g t; a) = a^{- (3 / 4) β + o (1)} exp (- \frac{2}{3} β a^{3 / 2}) .$