TY - JOUR

T1 - On some statistical models with a random number of observations

AU - Esquível, Manuel L.

AU - Mota, Pedro P.

AU - Tiago Mexia, João

N1 - This work was partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UID/MAT/00297/2013 (Centro de Matematica e Aplicacoes).

PY - 2016/10/1

Y1 - 2016/10/1

N2 - We extend some classical statistical inference to the case of a random number of observations with a stabilized distribution: namely, in the normal model, inference for the mean with known and unknown variance and inference for the variance. We describe some useful models for the number of observations obtained by truncation or translation of usual models given by integer-valued random variables: Poisson, binomial, geometric, and negative binomial. We present an efficient random search algorithm for the computation of the quantiles of the relevant statistics, we describe an interval estimation procedure for the extended model, and we propose a parametric bootstrap simulation study to validate the proposed procedure.

AB - We extend some classical statistical inference to the case of a random number of observations with a stabilized distribution: namely, in the normal model, inference for the mean with known and unknown variance and inference for the variance. We describe some useful models for the number of observations obtained by truncation or translation of usual models given by integer-valued random variables: Poisson, binomial, geometric, and negative binomial. We present an efficient random search algorithm for the computation of the quantiles of the relevant statistics, we describe an interval estimation procedure for the extended model, and we propose a parametric bootstrap simulation study to validate the proposed procedure.

KW - hypothesis tests power function

KW - interval estimation

KW - random number of observations

KW - Statistical inference

UR - http://www.scopus.com/inward/record.url?scp=84989960730&partnerID=8YFLogxK

U2 - 10.1080/15598608.2016.1227735

DO - 10.1080/15598608.2016.1227735

M3 - Article

AN - SCOPUS:84989960730

VL - 10

SP - 805

EP - 823

JO - Journal of Statistical Theory and Practice

JF - Journal of Statistical Theory and Practice

SN - 1559-8608

IS - 4

ER -