# Testing convexity of a discrete distribution

## TL;DR

This paper introduces two procedures based on convex least-squares estimation to test the convexity of a discrete probability distribution with unknown finite support, ensuring asymptotic calibration.

## Contribution

It presents novel testing procedures for convexity of discrete distributions using convex least-squares estimators, applicable when the support size is unknown.

## Key findings

- Procedures are asymptotically calibrated.
- Effective for distributions with unknown finite support.

## Abstract

Based on the convex least-squares estimator, we propose two different procedures for testing convexity of a probability mass function supported on N with an unknown finite support. The procedures are shown to be asymptotically calibrated.