Sequential Analysis and Robustness Study for the Parameters of Positive Exponential Family of Distributions with Known Coefficient of Variation

Surinder  Kumar; Prem  Lata Gautam; Vaidehi  Singh

Sequential Analysis and Robustness Study for the Parameters of Positive Exponential Family of Distributions with Known Coefficient of Variation

Authors

Surinder Kumar Department of Statistics, School for Physical and Decision Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow, India
Prem Lata Gautam Department of Statistics, School for Physical and Decision Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow, India
Vaidehi Singh Department of Statistics, School for Physical and Decision Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow, India

Keywords:

PEFD, sequential probability ratio test, operating characteristics, average sample number, acceptance and rejection regions, null hypotheses, alternative hypotheses, type I error and type II error

Abstract

In the present paper, we consider the positive exponential family of distributions, which has three
parameters $gif.latex?\theta&space;,\nu$ and $gif.latex?\rho&space;.$ On assigning different values to these parameters, it covers many distributions.
For the testing of hypotheses regarding the parameters $gif.latex?\theta$ and $gif.latex?\nu,$ a sequential testing procedures and
robustness of the operating characteristics and average sample number functions are derived. The
robustness of the sequential probability ratio test for the parameter $gif.latex?\theta&space;,$ when the coefficient of variation
is known are also obtained. The acceptance and rejection regions for the null hypotheses $gif.latex?H_0$ against
the alternative hypotheses $gif.latex?H_1$ are also studied and presented through a graph. The numerical values
of operating characteristics and average sample number function are presented in the tables and
graphs.

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Published

2022-09-29

How to Cite

Kumar, S. ., Lata Gautam, P. ., & Singh, V. . (2022). Sequential Analysis and Robustness Study for the Parameters of Positive Exponential Family of Distributions with Known Coefficient of Variation. Thailand Statistician, 20(4), 744–753. Retrieved from https://ph02.tci-thaijo.org/index.php/thaistat/article/view/247456