Unspecified distribution in single disorder problem

TL;DR

This paper addresses the problem of detecting a single disorder in a stochastic sequence with incomplete distribution information, transforming it into an optimal stopping problem and deriving decision formulas.

Contribution

It introduces a method for disorder detection under partial distribution knowledge and provides explicit formulas for optimal decision functions.

Findings

Derived formulas for optimal stopping rules.

Addressed disorder detection with incomplete distribution data.

Enhanced detection strategies in stochastic sequences.

Abstract

We register a stochastic sequence affected by one disorder. Monitoring of the sequence is made in the circumstances when not full information about distributions before and after the change is available. The initial problem of disorder detection is transformed to optimal stopping of observed sequence. Formula for optimal decision functions is derived.