On a waiting time distribution in a sequence of Bernoulli trials

DOI10.1007/BF00052333zbMath1002.60517OpenAlexW2103464964MaRDI QIDQ1373265

Markos V. Koutras

Publication date: 20 January 2003

Published in: Annals of the Institute of Statistical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00052333

Mathematics Subject Classification ID

Distribution theory (60E99)

Related Items (28)

Generalized waiting time distributions associated with runs ⋮ Joint distributions associated with patterns, successes and failures in a sequence of multi-state trials ⋮ Exact probability of fixed patterns occurring in a random sequence ⋮ Weak runs in sequences of binary trials ⋮ Simultaneous demonstration tests involving sparse failures ⋮ On the normal approximation for the distribution of the number of simple or compound patterns in a random sequence of multi-state trials ⋮ A family of induced distributions ⋮ A simple compound scan statistic useful for modeling insurance and risk management problems ⋮ Applications of Fuss-Catalan numbers to success runs of Bernoulli trials ⋮ A direct method to obtain the joint distribution of successes, failures and patterns in enumeration problems ⋮ From runs to patterns ⋮ The distributions of sum, minima and maxima of generalized geometric random variables ⋮ Generalizations of distributions related to \((k_1,k_2)\)-runs ⋮ Minimum and maximum distances between failures in binary sequences ⋮ Compound patterns and generating functions: from basic waiting times to counts of occurrence ⋮ Exact and asymptotic results for pattern waiting times ⋮ Approximating the extreme right-hand tail probability for the distribution of the number of patterns in a sequence of multi-state trials ⋮ Distributions of patterns of two successes separated by a string of \(k-2\) failures ⋮ Exact distribution of random order statistics and applications in risk management ⋮ Counting certain binary strings ⋮ Distribution of the length of the longest common subsequence of two multi-state biological sequences ⋮ Geometric distribution of order \(k\) with a reward ⋮ Distributions of simple patterns in some kinds of exchangeable sequences ⋮ Waiting time distributions of runs in higher order Markov chains ⋮ Asymptotic results for the multiple scan statistic ⋮ Limit theorems for a correlated moving window model ⋮ Unnamed Item ⋮ Accurate estimation for extra-Poisson variability assuming random effect models

Cites Work

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• The Negative Binomial Distribution of Orderk and Some of Its Properties
• Approximations and Bounds for the Distribution of the Scan Statistic
• Distribution Theory of Runs: A Markov Chain Approach
• Moving window detection for discrete data (Corresp.)
• Runs on a circle
• Some Results for Discrete Unimodality
• The Generalized Birthday Problem
• On the Occurrence of n Successes within N Bernoulli Trials
• On discrete distributions of order k

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