Exponential family distributions | Compound probability distributions | Factorial and binomial topics | Discrete distributions | Infinitely divisible probability distributions
In probability theory and statistics, the negative binomial distribution is a discrete probability distribution that models the number of failures in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of successes (denoted ) occurs. For example, we can define rolling a 6 on a die as a success, and rolling any other number as a failure, and ask how many failure rolls will occur before we see the third success. In such a case, the probability distribution of the number of failures that appear will be a negative binomial distribution. An alternative formulation is to model the number of total trials (instead of the number of failures). In fact, for a specified (non-random) number of successes (r), the number of failures (n - r) are random because the total trials (n) are random. For example, we could use the negative binomial distribution to model the number of days n (random) a certain machine works (specified by r) before it breaks down. The Pascal distribution (after Blaise Pascal) and Polya distribution (for George Pólya) are special cases of the negative binomial distribution. A convention among engineers, climatologists, and others is to use "negative binomial" or "Pascal" for the case of an integer-valued stopping-time parameter and use "Polya" for the real-valued case. For occurrences of associated discrete events, like tornado outbreaks, the Polya distributions can be used to give more accurate models than the Poisson distribution by allowing the mean and variance to be different, unlike the Poisson. The negative binomial distribution has a variance , with the distribution becoming identical to Poisson in the limit for a given mean . This can make the distribution a useful overdispersed alternative to the Poisson distribution, for example for a robust modification of Poisson regression. In epidemiology, it has been used to model disease transmission for infectious diseases where the likely number of onward infections may vary considerably from individual to individual and from setting to setting. More generally, it may be appropriate where events have positively correlated occurrences causing a larger variance than if the occurrences were independent, due to a positive covariance term. The term "negative binomial" is likely due to the fact that a certain binomial coefficient that appears in the formula for the probability mass function of the distribution can be written more simply with negative numbers. (Wikipedia).
Prob & Stats - Random Variable & Prob Distribution (44 of 53) Variance
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the variance of a binomial distribution. Next video in series: http://youtu.be/XWBCrgKkRnY
From playlist iLecturesOnline: Probability & Stats 2: Random Variable & Probability Distribution
Prob & Stats - Random Variable & Prob Distribution (37 of 53) Binomial Distribution
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain a basic understanding of binomial distribution. Next video in series: http://youtu.be/uO166WiwFFg
From playlist iLecturesOnline: Probability & Stats 2: Random Variable & Probability Distribution
The binomial is one of the basic distributions, yet surprisingly common in risk and quant finance. Here I take a look at its key properties and compare the formula to Excel's built in =BINOMDIST()
From playlist Statistics: Distributions
We use the Binomial Distribution app on ArtofStat.com to visualize the shape of the binomial distribution and to find probabilities for the number of successes in Bernoulli trials.
From playlist Chapter 6: Distributions
44 - Posterior predictive distribution a negative binomial for gamma prior to poisson likelihood
This video provides a derivation of the posterior predictive distribution - a negative binomial - for when there is a gamma prior to a Poisson likelihood. If you are interested in seeing more of the material on Bayesian statistics, arranged into a playlist, please visit: https://www.yout
From playlist Bayesian statistics: a comprehensive course
I created this video with the YouTube Video Editor (http://www.youtube.com/editor)
From playlist Probability Distributions
The Binomial Probability Distribution
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys The Binomial Probability Distribution
From playlist 5.2 Binomial Probability Distributions
Statistics Lecture 5.3: A Study of Binomial Probability Distributions
https://www.patreon.com/ProfessorLeonard Statistics Lecture 5.3: A Study of Binomial Probability Distributions
From playlist Statistics (Full Length Videos)
Variance of a Binomial Probability Distribution
Today, we derive the formula for the variance as well as the standard deviation of a binomial probability distribution.
From playlist Probability
Multiply Binomial with Higher Powers
This video explains how to multiply binomials with higher exponents. http://mathispower4u.com
From playlist Multiplying Polynomials
Multiplicaton of Polynomials (L3.4)
This video provides several examples of how to multiply polynomials. This video provides examples of how to solve geometry problems using polynomials.
From playlist Multiplying Polynomials
(2x + 1)(5x – 3) Find the Product of the BINMOIALS – 2 Ways
How to multiply binomials using the FOIL method. For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printable worksheets, review notes and quizzes.
From playlist GED Prep Videos
Ex 2: Polynomial Multiplication
This video provides four examples of how to multiply polynomials.
From playlist Multiplying Polynomials
How to Multiply Polynomials – NOT THAT DIFFICULT
Learn how to multiply polynomials. For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printable worksheets, review notes and quizzes. All courses
From playlist GED Prep Videos
Ex: Multiplying Binomial Conjugates with Fractions
This video explains how to multiply to binomial conjugates with fractions. http://mathispower4u.com
From playlist Multiplying Polynomials
distributive property, binomial multiplication (KristaKingMath)
► My Algebra 1 course: https://www.kristakingmath.com/algebra-1-course In this video we'll learn how to use the distributive property to multiply binomials. Distributive property tells us that we need to make sure that we multiply both terms in the first factor by both terms in the second
From playlist Algebra 1
Multiplying Binomials with Fraction Constants (ax+b/c)(dx+e/c)
This video explains how to multiply two binomials with fraction constants using repeated distribution. http://mathispower4u.com
From playlist Multiplying Polynomials
Ch9Pr18: Probability Distributions
A gentle introduction to probability distributions by looking at the uniform, binomial, geometric and Poisson distributions. This is Chapter 9 Problem 18 from the MATH1231/1241 Algebra notes. Presented by Thomas Britz from UNSW.
From playlist Mathematics 1B (Algebra)
Extra Math Lecture 2: The mean of the binomial distribution
Forelæsning med Per B. Brockhoff. Kapitler:
From playlist DTU: Introduction to Statistics | CosmoLearning.org
FRM: Quantile function (Inverse CDF)
Here is the spreadsheet I used (and that shows the same recursive solution to all three distributions): http://db.tt/gyrCxFU5 The quantile function, which is the inverted cumulative distribution function, gives us the value (X) that answers the question, with confidence of (P%), what is th
From playlist Operational Risk Analytics