Search for tag: "distribution"

Estimation and Testing with Normal Errors

In this lesson, the assumption of the normality of errors, and hence the normality of the responses is added to the simple linear regression model. The consequences are that maximum likelihood…

From  Jane Harvill 43 plays 0  

Bayesian Credible Sets

So far, the interval estimators we have discussed are frequentists methods. In this lesson, we discuss Bayesian credible sets - the correct name for Bayesian "confidence intervals." In…

From  Jane Harvill 112 plays 0  

Example: Find Confidence Interval by Inverting CDF of an Estimator

A confidence interval estimator for the shift parameter is found by inverting the CDF of a sufficient statistic for the parameter.

From  Jane Harvill 467 plays 0  

Finding Interval Estimators

In this first lesson on interval estimation, we address three methods in the frequentist domain for finding interval estimators. The first is the inversion of a test statistic, the second is using…

From  Jane Harvill 308 plays 0  

Bayesian Tests

The method for finding a Bayesian test depends on the posterior of the parameter and a function of the data. Using the posterior probabilities of the null parameter space and the alternative…

From  Jane Harvill 144 plays 0  

Find the Bayes estimator of the rate of a Poisson distribution

This example illustrates how to find the Bayes estimator, under squared error loss function, of the rate of a Poisson distribution if the prior distribution on the rate is a gamma distribution.

From  Jane Harvill 220 plays 0  

Find the MLE of the rate of a Poisson distribution

Example to illustrate finding the maximum likelihood estimator of the rate of a Poisson distribution.

From  Jane Harvill 312 plays 0  

Finding the maximum likelihood estimator of the upper bound of a uniform(0, B) distribution

This example illustrates how to find the maximum likelihood estimator (MLE) of the upper bound of a uniform(0, B) distribution. In this example, calculus cannot be used to find the MLE since the…

From  Jane Harvill 956 plays 0  

Bayes Estimation: A Review

In statistical inference, the frequentist perspective considers the parameter θ to be a fixed, but unknown quantity. Statistics used for inferential purposes ideally have specific optimal…

From  Jane Harvill 107 plays 0  

Illustrate Finding the Joint PDF of Sample from Exponential Family

An example to illustrate how to find the joint probability density function of a random sample from a gamma distribution using the result that the gamma family of distributions is an exponential…

From  Jane Harvill 99 plays 0  

Show gamma family of PDFs is an exponential family

Example to show that the gamma family of PDFs is an exponential family

From  Jane Harvill 1,001 plays 0  

Bayes Estimators

The Bayesian approach to statistics is fundamentally different from the classical approach that we have been discussing. However, some aspects of the Bayesian approach can be quite helpful to other…

From  Jane Harvill 257 plays 0  

Data Reduction and Sufficiency

The information in a random sample is used to make inferences about an unknown parameter theta. If the sample size n is large, then the observed sample is a long list of numbers that is difficult, if…

From  Jane Harvill 374 plays 0  

The Delta Method

The previous lesson on convergence concepts primarily focused on results as they apply to the sample mean or to a standardized random variable having a limiting normal distribution. There are times…

From  Jane Harvill 416 plays 0  

Convergence Concepts

In this lesson, the effect of allowing the sample size n to increase to infinity is considered. Although this idea is not practical, it does provide useful approximations for the finite-sample case.…

From  Jane Harvill 315 plays 0  

Order Statistics

Sample values such as the smallest, largest, or middle observations from a random sample can provide additional summary information. The minimum, maximum, or median are all examples of order…

From  Jane Harvill 195 plays 0  

Sampling from a Normal Distribution

In previous lessons, properties of samples and of statistics computed on a random sample were discussed under a very general framework; in other words, under the idea that a random sample is selected…

From  Jane Harvill 86 plays 0  

Sums of Random Variables from a Random Sample

When a random sample is drawn, some summary of the values is usually computed. Any well-defined summary may be expressed mathematically as a function of an n-dimension vector. The domain of that…

From  Jane Harvill 183 plays 0  

Covariance and Correlation

In earlier lessons, we discussed the absence or presence of a relationship between variables, and how to model that relationship. We discussed joint probability functions, conditional probability…

From  Jane Harvill 68 plays 0  

Conditional Distributions and Independence

Oftentimes when two random variables (X, Y) are observed, the values of the two variables are related. For example, it may be that knowledge about the value of X gives information about the value of…

From  Jane Harvill 170 plays 0  

Joint and Marginal Distributions, Continuous Case

The previous lesson concluded with joint and marginal distributions for the discrete case. We now consider the same concepts, but for continuous random vectors. While discrete random vectors and the…

From  Jane Harvill 153 plays 0  

Joint and Marginal Distributions, Discrete Case

All of the models previously discussed involved only one random variable and were called univariate models. We now move forward and discuss probability models that involve more than one random…

From  Jane Harvill 105 plays 0  

Beta Distribution

The beta distribution is the last continuous distribution we will discuss. Like the gamma distribution, the beta distribution earns its name from being associated with the beta function. The beta…

From  Jane Harvill 45 plays 0  

Normal Distribution

In this lesson, we learn about the most important distribution in statistics - the normal distribution. We investigate the probability density function and cumulative distribution function and the…

From  Jane Harvill 61 plays 0  

Gamma Distribution

The gamma family of distributions is a very special family that has many distributions as a specific case. In this lesson, we begin with the gamma function. We then introduce the gamma…

From  Jane Harvill 254 plays 0  

Uniform Distribution

An overview of the uniform distribution is given, including its probability density function (PDF) and cumulative distribution function (CDF). The mean, variance, and moment generating function are…

From  Jane Harvill 75 plays 0  

Continuous Distributions: A Review

In this lesson, a brief review of the general properties of continuous distributions is provided. The end of the lesson is a comparison of the properties for continuous and discrete distributions.

From  Jane Harvill 59 plays 0  

Poisson Distribution

The Poisson distribution is different from all of the discrete distributions we have considered up until this point. Instead of counting the number of "successes" or counting the number of…

From  Jane Harvill 51 plays 0  

Negative Binomial Distribution

The negative binomial distribution is an extension of the geometric distribution, and so is also related to the Bernoulli distribution. Whereas the geometric distribution results from counting the…

From  Jane Harvill 162 plays 0  

Hypergeometric Distribution

The experiment that is used to illustrate when the hypergeometric distribution arises is that of an urn with N balls of two colors; M "white" balls and N - M "black" balls. The…

From  Jane Harvill 86 plays 0  

Geometric Distribution

Like the binomial and hypergeometric distributions, the geometric distribution is related to the Bernoulli(p) distribution. Unlike the binomial and hypergeometric distributions, the geometric…

From  Jane Harvill 44 plays 0  

Binomial Distribution

The binomial distribution is introduced through its unique connection to the Bernoulli distribution through what is called a Bernoulli process. The probability mass function is derived and proven to…

From  Jane Harvill 75 plays 0  

Bernoulli Distribution

The Bernoulli and binomial distributions are used for modeling a dichotomous experiment or a sequence of independent dichotomous experiments, respectively. Alone, both distributions apply to a wide…

From  Jane Harvill 56 plays 0  

Discrete Uniform Distribution

The discrete uniform distribution is one of the simplest discrete distributions. In this lesson, the distribution is defined via its probability mass function. The cumulative distribution function…

From  Jane Harvill 88 plays 0  

Discrete Distributions: A Review

In this lesson, a brief review of the general properties of discrete distributions is provided.

From  Jane Harvill 50 plays 0  

Probability Density Functions

In this lesson, probability density functions are introduced, defined, and discussed. Properties of probability mass functions and probability density functions are presented. Concepts are…

From  Jane Harvill 133 plays 0  

Distribution Functions

This lesson is the first of many that discuss probability functions. We begin the discussion of probability functions with the cumulative distribution function (CDF). The CDF is defined and…

From  Jane Harvill 120 plays 0  

Dr. Margaret M. Mitchell - Did Paul Really Mean that the Reason We Should Feed our Enemies is "To Heap Burning Coals on their Heads" (Romans 12:20)?

Parchman Endowed Lectures October 25, 2016

From  Nicholas Hunt 159 plays

Abigail Higgins - An Arbiter of Rights? The Role of the Divine in Locke, Paine, and Jefferson - 2016 Panel 4

2016 Baylor Libraries Symposium: Thomas Paine's Rights of Man Panel Five 2016 September 30 Abigail Higgins An Arbiter of Rights? The Role of the Divine in Locke, Paine, and Jefferson

From  Christina Chan-Park 22 plays 0  

Dr. Brad Owens - W.R. "Bob" Poage: Retail Politics in Wartime - 2016 Panel 5

2016 Baylor Libraries Symposium: Thomas Paine's Rights of Man Panel Five 2016 September 30 Dr. Brad Owens W.R. "Bob" Poage: Retail Politics in Wartime

From  Christina Chan-Park 20 plays 0