Chapter 20: Non-Normal Probability Distributions
Reviewing Normal Probability Distributions
Normal distribution is related to continuous data & discrete data is not continuous in nature
Anatomy of a Normal Curve: a normal curve is typically symmetrical in nature, data elements concentrate along center of curve, it is described statistically using mean and standard deviation
Non-Normal Continuous Distributions
Exponential Distribution: creates a histogram or trend line that is exponential in nature, decreases exponentially as you travel along x-axis
Lognormal Distribution: used when working with data sets that describe time durations such as the time a process or machine is down, or distribution of assets or wealth amon a population, it is assymetrical on a histogram
Weilbull Distribution: relates to continuous data and data does not fit discrete data distribution, describes many data and used when working with reliability applications and failure probabilities that change or vary with time
Other Types of Continuous Distributions
Central Limit Theorem: distribution of the mean of a large, identically distributed number of independed variables will approximate the normal curve
Cauchy Distribution: looks like elongated normal curve with tighter peak, doesn't have a defined mean or variance
Logistic Distribution: similar to normal curve, CDF is more consistently calculable
Cumulative Density Function (CDF): calculates probability that a given data point is less equal than or equal to X, where X is any point on the x-axis of the curve
Laplace Distribution: referred to as bilateral exponential distribution or double exponential distribution
Uniform Distribution: occurs when data points are divided evenly among bins, never occurs in a random sample
Beta Distribution: can take on a number of shapes, considered extremely flexible and can become stand-ins or other distributions
Gamma: take on a number of shapes, always skewed to right
Triangular Distribution: formed using mode and upper and lower limits of data sets
Non-Normal Discrete Distributions
Binomial Distribution: used when dealing with discrete data, two outcomes for each trial or sample, outcome of any given trial is independent of outcome of another trial
Poisson Distribution: used when dealing with data that is distributed randomly within time, distance, or any other unit of measurement
Other Types of Discrete Distribution
Geometric Distribution: used when there are two outcomes for a trial, trials are independent, and there is waiting time before the first occurrence
Negative Binomial: used with attribute data-fail/pass and other situations where there are only two outcomes for each trial
Applying Data to Real-World Situations: many of the statistical analyses performed on data will be related to normal curve