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Some Bayesian lower bounds on reliability in the lognormal distribution
Author(s) -
Padgett W. J.,
Johnson M. P.
Publication year - 1983
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3314981
Subject(s) - log normal distribution , bayesian probability , mathematics , reliability (semiconductor) , gamma distribution , monte carlo method , prior probability , statistics , function (biology) , distribution (mathematics) , probability density function , statistical physics , combinatorics , physics , mathematical analysis , thermodynamics , power (physics) , evolutionary biology , biology
The two‐parameter lognormal distribution with density function f(y : γ, σ 2 ) = [(2πσ 2 ) 1/2 y ] 1 exp[−(ln y − γ) 2 /2σ 2 ], y > 0, is important as a failure‐time model in life testing. In this paper, Bayesian lower bounds for the reliability function R(t : γ, σ 2 ) = ϕ[(γ − ln t )/σ] are obtained for two cases. First, it is assumed that γ is known and σ 2 has either an inverted gamma or “general uniform” prior distribution. Then, for the case that both γ and σ 2 are unknown, the normal‐gamma prior and Jeffreys' vague prior are considered. Some Monte Carlo simulations are given to indicate some of the properties of the Bayesian lower bounds.