Statistical Distribution REview

1: Why Distribution?

• Distribution reflects a STRONG PATTERN in the DATA!!
• In some cases, Patterns are more important to study then DATA itself.

2: What is Distribution?

• Cumulative Distribution Function (CDF)
• Probability Mass Function (PMF) 
• Probability Distribution Function (PDF)

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Common Distributions and When to USE:

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3. Normal Distribution

When?

• If a variable depends on a large number of independent non-dominating parameters, the variable tends to follow Normal (Gaussian) Distribution. e.g
• Measure noise
• Human heights
• Exam grades

What is like? [Two parameter distribution]

Standard Normal Distribution: N(0, 1)

4. Uniform Distribution

When?

• Each value in X has the same possibility.

5. Exponential Distribution (Continuous)

When? 

• model the waiting time for the next event to happen, e.g.
• the next vehicle passing a line
• bank service time duration

What?

6. Geometric Distribution (Discrete)

When

• Fail times util success Once, similar with Exponential

What

7. Binomial distribution (Discrete)

When

• Try N times and success K times
• When  N -> INFINITY, it becomes Normal

What

8. Poisson Distribution

When

• Counts of random events, e.g.
• number of phone calls received one day

What

9. Chi-2 Distribution

Definition

X1^2 + X2^2 + X3^2 + ... + Xk^2

Given,

Xi ~ N(0, 1)

When

Testing

What

10. F-Distribution

When

What

11. T-Distribution