Eikosstatistics & data science

Probability & Statistical Inference · Stochastic Processes

Renewal theory · Stochastic processes

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Advanced theory module

Overview

Topics covered

  • Introduction
  • Renewal Theory: analysis of events in continuous time
  • Introduction, origin and history of the Renewal Theory
  • Formal definition of a renewal process
  • The distribution of N(t) and characterization by convolution
  • Exponential Case

Related concepts

Main connections

  • Calculus & differentiation
  • Mathematical expectation & moments
  • Mean & expected value
  • Poisson distribution
  • Bayes' theorem & priors
  • Central limit theorem

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

S0=0,Sn=∑i=1nXifor n≥1.
View LaTeX sourceS_0 = 0, \qquad S_n = \sum_{i=1}^n X_i \quad \text{for } n \ge 1.