Bivariate gamma distribution as a life test model

Giri S. Lingappaiah

Displaying similar documents to “Bivariate gamma distribution as a life test model”

Generalized length biased distributions

Giri S. Lingappaiah (1988)

Aplikace matematiky

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Generalized length biased distribution is defined as $h (x) = φ_{r} (x) f (x), x > 0$ , where $f (x)$ is a probability density function, $φ_{r} (x)$ is a polynomial of degree $r$ , that is, $φ_{r} (x) = a_{1} (x / μ_{1}^{'}) + ... + a_{r} (x^{r} / μ_{r}^{'})$ , with $a_{i} > 0, i = 1, ..., r, a_{1} + ... + a_{r} = 1, μ_{i}^{'} = E (x^{i})$ for $f (x), i = 1, 2 ..., r$ . If $r = 1$ , we have the simple length biased distribution of Gupta and Keating [1]. First, characterizations of exponential, uniform and beta distributions are given in terms of simple length biased distributions. Next, for the case of generalized distribution, the distribution of the sum of $n$ independent variables is put in the closed...

A method constructing density functions: the case of a generalized Rayleigh variable

Viorel Gh. Vodă (2009)

Applications of Mathematics

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In this paper we propose a new generalized Rayleigh distribution different from that introduced in Apl. Mat. (1976), pp. 395–412. The construction makes use of the so-called “conservability approach” (see Kybernetika (1989), pp. 209–215) namely, if $X$ is a positive continuous random variable with a finite mean-value $E (X)$ , then a new density is set to be $f_{1} (x) = x f (x) / E (X)$ , where $f (x)$ is the probability density function of $X$ . The new generalized Rayleigh variable is obtained using a generalized form of the...

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....

On the outstanding elements and record values in the exponential and gamma populations.

G. S. Lingappaiah (1981)

Trabajos de Estadística e Investigación Operativa

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Outstanding elements and recorded values are discussed in this paper as related to exponential and gamma populations. First, the problem of prediction is considered when there are available, k sets of independent observations from a general-type exponential distribution. In such a case, prediction of the n-th record value in the k-th set is made in terms of n-th (i = 1, ..., k-1) record values from other (k-1) sets. For this purpose a predictive distribution is obtained. Secondly, the...

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 new weighted Gompertz distribution with applications to reliability data

Hassan S. Bakouch, Ahmed M. T. Abd El-Bar (2017)

Applications of Mathematics

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A new weighted version of the Gompertz distribution is introduced. It is noted that the model represents a mixture of classical Gompertz and second upper record value of Gompertz densities, and using a certain transformation it gives a new version of the two-parameter Lindley distribution. The model can be also regarded as a dual member of the log-Lindley- $X$ family. Various properties of the model are obtained, including hazard rate function, moments, moment generating function, quantile...