Records via Probability Theory by Mohammad Ahsanullah & Valery B. Nevzorov

Author:Mohammad Ahsanullah & Valery B. Nevzorov
Language: eng
Format: epub
Publisher: Atlantis Press, Paris

7.4.1 The Minimum Variance Linear Unbiased Estimate of α and β When γ Is Known and

Suppose X(1), X(2),…, X(m) be the first m upper records from this distribution.

Let

with X(0) = 0, and

Now

Let , then , where

We can write X′X as

Theorem 7.4.1.1

The minimum variance linear unbiased estimates of α and β respectively based on Y1,…, Yn (assuming γ as known and γ ≠ 0 are)

On simplification, we get

The variances and covariance of are given by

and

7.4.2 Minimum Variance Linear Invariance Estimators

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