Minimum risk sequential point estimation of the stress-strength reliability parameter for exponential distribution

In this article, the tampered failure rate model is used in partially accelerated life testing. A non-decreasing time function, often called a ‘‘time transformation function", is proposed to tamper the failure rate under design conditions. Different types of the proposed function, which have sufficient conditions in order to be accelerating functions, are investigated. A baseline failure rate of the exponential distribution is considered. Some point estimation methods, as well as approximate confidence intervals, for the parameters involved are discussed based on generalized progressively hybrid censored data. The determination of the optimal stress change time is discussed under two different criteria of optimality. A real dataset is employed to explain the theoretical outcomes discussed in this article. Finally, a Monte Carlo simulation study is carried out to examine the performance of the estimation methods and the optimality criteria.

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On the Asymptotic Regret While Estimating the Location of an Exponential Distribution

Calcutta Statistical Association Bulletin ◽

10.1177/0008068319820310 ◽

1982 ◽

Vol 31 (3-4) ◽

pp. 207-214 ◽

Cited By ~ 16

Author(s):

Nitis Mukhopadhyay

Keyword(s):

Exponential Distribution ◽

Location Parameter ◽

Point Estimation ◽

Sequential Procedure ◽

Asymptotic Behaviors

Mukhopadhyay's (1974) sequential procedure for estimating the location parameter of a negnive exponential distribution is further analyzed in the case of point estimation. Two main results are summarized in Theorems 1 and 2, and sbcse study asymptotic behaviors of the “regret”.

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On Sequential Procedures for the Point Estimation of the Mean Vector

Calcutta Statistical Association Bulletin ◽

10.1177/0008068319880105 ◽

1988 ◽

Vol 37 (1-2) ◽

pp. 47-54 ◽

Cited By ~ 6

Author(s):

R. Karan Singh ◽

Ajit Chaturvedi

Keyword(s):

Normal Population ◽

Stopping Time ◽

Point Estimation ◽

Multivariate Normal ◽

Minimum Risk ◽

Sequential Procedures ◽

Multivariate Normal Population ◽

Bounded Risk ◽

The Mean ◽

Mean Vector

Sequential procedures are proposed for (a) the minimum risk point estimation and (b) the bounded risk point estimation of the mean vector of a multivariate normal population . Second-order approximations are derived. For the problem (b), a lower bound for the number of additional observations (after stopping time) is obtained which ensures “ exact” boundedness of the risk associated witb the sequential procedure.

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Sequential point and interval estimation of scale parameter of exponential distribution

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171295000470 ◽

1995 ◽

Vol 18 (2) ◽

pp. 383-390

Author(s):

Z. Govindarajulu

Keyword(s):

Exponential Distribution ◽

Scale Parameter ◽

Stopping Time ◽

Interval Estimation ◽

Location Parameter ◽

Exact Expression ◽

Point Estimation ◽

Quadratic Loss ◽

Negative Exponential Distribution ◽

Negative Exponential

Sequential fixed-width confidence intervals are obtained for the scale parameterσwhen the location parameterθof the negative exponential distribution is unknown. Exact expressions for the stopping time and the confidence coefficient associated with the sequential fixed-width interval are derived. Also derived is the exact expression for the stopping time of sequential point estimation with quadratic loss and linear cost. These are numerically evaluated for certain nominal confidence coefficients, widths of the interval and cost functions, and are compared with the second order asymptotic expressions.

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