Continuous Distributions

If the data is classified as Continuous, the following are links to most common Continuous Distributions used in Six Sigma projects.

A continuous probability distribution is one in which a continuous random variable X can take on any value within a given range of values. The amount of values can be infinite.

For example, measuring the temperate in degrees can be take on an infinite number of values depending on how many decimals you allow. However if the scale is COLD, WARM, and HOT then the data is Discrete. You can see how continuous data can provide more information than discrete data.

Examples:

The amount of time (in hours, minutes, and seconds) to run a race. A discrete option may be SLOW, FAST, FASTER, FASTEST.
The height of people.
The weight of a something in Kg. The discreate binomial option may be LIGHT or HEAVY
The speed of a commuter train.

A BB/GB should be familiar with the following:

1) Uniform Distribution
2) Normal Distribution
3) Exponential Distribution
4) T Distribution
5) Chi-Square Distribution
6) F Distribution

A few other continuous distributions are the Beta, Erlang, Gamma, Cauchy, Lognormal, Weibull, Double Exponential, Power Normal, Power Log Normal, Bivariate Normal, Logistic, Gumbel, and Tukey-Lambda.

Click here for an overview of Discrete Distributions.

Beta and Binomial Distributions

Differences between the Beta and Binomial Distributions

Binomial is discrete, dealing with counts (number of successes), two outcomes.
Beta is continuous, dealing with probabilities. on the interval from [0,1].
Binomial models the probability of x successes in n trials, given the probability of success p.
Beta models the probability distribution of the parameter p itself. Often used to represent processes with natural lower and upper limits.

Examples:

Binomial: There are two outcomes such as a coin flip. What's the probability of getting exactly 4 tails out of 10 flips?
Beta: Imagine you don't know the probability of getting tails (p) but you have some prior belief about it. The Beta distribution can model the possible values of p.

Visually:

Binomial:. A histogram or bar chart, showing the probability of each possible number of successes.
Beta: A curve, showing the probability density at each possible value of the probability p.

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