# Interval Estimation of the Unknown Exponential Parameter Based on Time Truncated Data

## TL;DR

This paper develops new statistical methods for estimating the unknown parameter of an exponential distribution using time truncated data, common in reliability testing, providing results based on an unconditional approach and extending to two-parameter distributions.

## Contribution

It introduces unconditional inference methods for exponential parameters from time truncated data and extends these methods to two-parameter distributions, unlike previous conditional approaches.

## Key findings

- Unconditional inference results for exponential distribution parameters.
- Extensions to two-parameter distributions.
- Applicable to reliability analysis with censored data.

## Abstract

In this paper we consider the statistical inference of the unknown parameter of an exponential distribution based on the time truncated data. The time truncated data occurs quite often in the reliability analysis for type-I or hybrid censoring cases. All the results available today are based on the conditional argument that at least one failure occurs during the experiment. In this paper we provide some inferential results based on the unconditional argument. We extend the results for some two-parameter distributions also.