THE POISSON THEOREM FOR BERNOULLI TRIALS WITH A RANDOM PROBABILITY OF SUCCESS AND A DISCRETE ANALOG OF THE WEIBULL DISTRIBUTION

2016 ◽  
Keyword(s):  
Weibull Distribution ◽  
Discrete Analog ◽  
Bernoulli Trials ◽  
Probability Of Success ◽  
Random Probability

Extensions of the Hájek–Rényi inequality to moments of higher order

1972 ◽  
Vol 72 (1) ◽  
pp. 67-75
Author(s):  
J. E. A. Dunnage
Keyword(s):  
Higher Order ◽  
Bernoulli Trials ◽  
Probability Of Success ◽  
Image Position

1. Introduction. Bernoulli trials. Consider a sequence of Bernoulli trials. Let p, assumed to satisfy 0<p < 1, be the probability of success at any given trial and let q = 1–p. If Nn is the number of successes in the first n trials, it is well known that Nn/n→p almost surely as n→∞ so that for every ∈> 0,as n→∞, and it is clearly of great interest to know quantitatively how this probability depends upon n and ∈.

scholarly journals The Number of Two Consecutive Successes in a Hoppe-Pólya Urn

2008 ◽  
Vol 45 (3) ◽  
pp. 901-906 ◽  
Author(s):  
Lars Holst
Keyword(s):  
Explicit Formula ◽  
Bernoulli Trials ◽  
Pólya Urn ◽  
Probability Of Success ◽  
Polya Urn ◽  
Binomial Moments

In a sequence of independent Bernoulli trials the probability of success in the kth trial is pk = a / (a + b + k − 1). An explicit formula for the binomial moments of the number of two consecutive successes in the first n trials is obtained and some consequences of it are derived.

scholarly journals THE BETA-WEIBULL DISTRIBUTION ON THE LATTICE OF INTEGERS

2016 ◽  
Vol 39 (1) ◽  
pp. 40 ◽  
Author(s):  
Vahid Nekoukhou ◽  
Hamid Bidram ◽  
Rasool Roozegar
Keyword(s):  
Weibull Distribution ◽  
Hazard Rate ◽  
Real Data ◽  
Rate Function ◽  
Discrete Analog ◽  
Discrete Distributions ◽  
Hazard Rate Function ◽  
Data Set ◽  
Beta Weibull Distribution ◽  
New Distribution

In this paper, a discrete analog of the beta-Weibull distribution is studied. This new distribution contains several discrete distributions as special sub-models. Some distributional and moment properties of the discrete beta-Weibull distribution as well as its order statistics are discussed. We will show that the hazard rate function of the new model can be increasing, decreasing, bathtub-shaped and upside-down bathtub. Estimation of the parameters is illustrated and the model with a real data set is also examined.

scholarly journals The Number of Two Consecutive Successes in a Hoppe-Pólya Urn

2008 ◽  
Vol 45 (03) ◽  
pp. 901-906 ◽  
Author(s):  
Lars Holst
Keyword(s):  
Explicit Formula ◽  
Bernoulli Trials ◽  
Pólya Urn ◽  
Probability Of Success ◽  
Polya Urn ◽  
Binomial Moments

In a sequence of independent Bernoulli trials the probability of success in the kth trial is p k = a / (a + b + k − 1). An explicit formula for the binomial moments of the number of two consecutive successes in the first n trials is obtained and some consequences of it are derived.

Brownian motion with quadratic killing and some implications

1986 ◽  
Vol 23 (04) ◽  
pp. 893-903 ◽  
Author(s):  
Michael L. Wenocur
Keyword(s):  
Brownian Motion ◽  
Weibull Distribution ◽  
Special Function ◽  
Function Theory ◽  
Killing Rate

Brownian motion subject to a quadratic killing rate and its connection with the Weibull distribution is analyzed. The distribution obtained for the process killing time significantly generalizes the Weibull. The derivation involves the use of the Karhunen–Loève expansion for Brownian motion, special function theory, and the calculus of residues.

A Latent State-Trait Analysis of Current Achievement Motivation Across Different Tasks of Cognitive Ability

2017 ◽  
Vol 33 (5) ◽  
pp. 318-327
Author(s):  
Philipp Alexander Freund ◽  
Vanessa Katharina Jaensch ◽  
Franzis Preckel
Keyword(s):  
Cognitive Ability ◽  
Task Performance ◽  
Achievement Motivation ◽  
Fear Of Failure ◽  
Specific Task ◽  
Test Taker ◽  
Specific Interest ◽  
Probability Of Success ◽  
Ability Tests ◽  
Perceived Challenge

Abstract. The current study investigates the behavior of task-specific, current achievement motivation (CAM: interest in the task, probability of success, perceived challenge, and fear of failure) across a variety of reasoning tasks featuring verbal, numerical, and figural content. CAM is conceptualized as a state-like variable, and in order to assess the relative stability of the four CAM variables across different tasks, latent state trait analyses are conducted. The major findings indicate that the degree of challenge a test taker experiences and the fear of failing a given task appear to be relatively stable regardless of the specific task utilized, whereas interest and probability of success are more directly influenced by task-specific characteristics and demands. Furthermore, task performance is related to task-specific interest and probability of success. We discuss the implications and benefits of these results with regard to the use of cognitive ability tests in general. Importantly, taking motivational differences between test takers into account appears to offer valuable information which helps to explain differences in task performance.

Sign in / Sign up

Export Citation Format

Share Document