More probability distributions

Introduction to Statistics in R

Maggie Matsui

Content Developer, DataCamp

Exponential distribution

Probability of time between Poisson events
Examples
- Probability of > 1 day between adoptions
- Probability of < 10 minutes between restaurant arrivals
- Probability of 6-8 months between earthquakes
Also uses lambda (rate)
Continuous (time)

On average, one customer service ticket is created every 2 minutes
- $\lambda$ = 0.5 customer service tickets created each minute

Exponential distribution with lambda = 0.5

3 Exponential distributions with lambda = 0.5, lambda = 1, and lambda = 1.5

$P(\text{wait} < \text{1 min})$ =

pexp(1, rate = 0.5)

0.3934693

$P(\text{wait} > \text{4 min})$ =

pexp(4, rate = 0.5, lower.tail = FALSE)

0.1353353

$P(\text{1 min} < \text{wait} < \text{4 min})$ =

pexp(4, rate = 0.5) - pexp(1, rate = 0.5)

0.4711954

In terms of rate (Poisson):

In terms of time (exponential):

t-distribution and normal distribution plotted on same axes

Has parameter degrees of freedom (df) which affects the thickness of the tails
- Lower df = thicker tails, higher standard deviation
- Higher df = closer to normal distribution

3 t distributions with df = 1, df = 5, and df = 10

Variable whose logarithm is normally distributed
Examples:
- Length of chess games
- Adult blood pressure
- Number of hospitalizations in the 2003 SARS outbreak

3 log-normal distributions with sd = 0.5, sd = 1, and sd = 1.5

Introduction to Statistics in R