TY - JOUR

T1 - Application of laplace approximation to record values

AU - Basak, Prasanta

AU - Bagchi, Parthasarathy

N1 - Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

PY - 1990

Y1 - 1990

N2 - Let Y1, Y2…,Yn,. be a sequence of independent and identically distributed random variables with a continuous distribution function F(y) and corresponding probability density function f(y). If {K(n), n > 1} is defined by K(1) = 1, K(n) = min{j|j > K(n - 1),Yj > YK(n- 1)} for n > 2, then (Y(n) = F/K(n),n > 1} is said to be a sequence of record values, We develop accurate approximations based on the Laplace approximation method as developed by Tierney and Kadane (1986) to the predictive distribution of a future observation based on (1) the availability of just a sequence of record values, and (2) the full likelihood. It is seen that this approximation is remarkable in small sample sizes leading to tractable results for any distribution of the observations.

AB - Let Y1, Y2…,Yn,. be a sequence of independent and identically distributed random variables with a continuous distribution function F(y) and corresponding probability density function f(y). If {K(n), n > 1} is defined by K(1) = 1, K(n) = min{j|j > K(n - 1),Yj > YK(n- 1)} for n > 2, then (Y(n) = F/K(n),n > 1} is said to be a sequence of record values, We develop accurate approximations based on the Laplace approximation method as developed by Tierney and Kadane (1986) to the predictive distribution of a future observation based on (1) the availability of just a sequence of record values, and (2) the full likelihood. It is seen that this approximation is remarkable in small sample sizes leading to tractable results for any distribution of the observations.

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U2 - 10.1080/03610929008830297

DO - 10.1080/03610929008830297

M3 - Article

AN - SCOPUS:84972899534

SN - 0361-0926

VL - 19

SP - 1875

EP - 1888

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

IS - 5

ER -