Abstract
In this paper, we discuss the record values arising from the Lindley distribution. We compute the means, variances and covariances of the record values. These values are used to compute the best linear unbiased estimators (BLUEs) and the best linear invariant estimators (BLIEs) of the location and scale parameters. By using the BLUEs and BLIEs, we construct confidence intervals for the location and scale parameters through Monte Carlo simulations. Prediction for the future records is also discussed.
Highlights
Let X1, X2, ⋯ be a sequence of independent and identically distributed (IID) random variables with cumulative distribution function F (x) and probability density function f (x)
An observation Xj is an upper record value of this sequence if it exceeds in value all preceding observations, i.e., if Xj > Xi, ∀i < j
The sequence of record statistics can be viewed as order statistics from a sample whose size is determined by the values and the order of occurrence of the observations
Summary
Let X1, X2, ⋯ be a sequence of independent and identically distributed (IID) random variables with cumulative distribution function (cdf) F (x) and probability density function (pdf) f (x). Asgharzadeh et al [20] discussed the maximum likelihood and Bayesian estimation of the shape parameter of the Lindley distribution based on upper records. Variances and covariances of the upper record values We use these moments to calculate best linear unbiased estimators (BLUEs) and best linear invariant estimators (BLIEs) for the location and scale parameters of the Lindley distribution. Ahsanullah [21] and Dunsmore [22] discussed the BLUEs and prediction of future record values from a two-parameter exponential distribution.
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