# Updated fiducial distribution of parameters in the associated delta-lognormal population

## TL;DR

This paper introduces a new statistical method for analyzing data with zero observations using an updated delta-lognormal distribution.

## Contribution

The paper proposes an exact sampling method and updated fiducial distributions for improved parameter inference.

## Key findings

- The proposed goodness-of-fit test ensures data compatibility with the delta-lognormal distribution.
- The updated fiducial distributions yield asymptotically correct confidence intervals and hypothesis testing levels.
- Simulation studies show significant improvement in parameter inference using the new method.

## Abstract

In this paper we consider a special kind of semicontinous distribution. We try to concern with the situation where the probability of zero observation is associated with the location and scale parameters in lognormal distribution. We first propose a goodness-of-fit test to ensure that the data can be fit by the associated delta-lognormal distribution. Then we define the updated fiducial distributions of the parameters and establish the results that the confidence interval has asymtotically correct level while the significance level of the hypothesis testing is also asymtotically correct. We propose an exact sampling method to sample from the updated fiducial distribution. It can be seen in our simulation study that the inference on the parameters is largely improved. A real data example is also used to illustrate our method.