Probability distributions
- A probability distribution describes how the values of a random variable are distributed.
- It assigns a probability to each possible outcome of a process or experiment that is assumed random. The random variable can be continuous or discrete.
- Probability distributions can be very useful because, since the characteristics of each distribution are well understood, they can be used to, using a sample of observations, make statistical inferences on the entire population.
- A probability distribution can be specified in a number of ways:
- Through a probability density function (probability mass function)
- Through a cumulative distribution function (survival function)
- Through a hazard function
- Through a characteristic function
- Some common distributions include:
- Binomial distribution: dbinom()
- The collection of possible outcomes of a coin toss [H|T] follow a
- Cauchy distribution: dcauchy()
- Chi-squared distribution: dchisq()
- Exponential distribution: dexp()
- F distribution: df()
- Gamma distribution: dgamma()
- Hypergeometric distribution: dhyper()
- Log-normal distribution: dlnorm()
- Geometric distribution: dgeom()
- Multinomial distribution: dmultinom()
- Negative binomial distribution: dnbinom()
- Normal distribution: dnorm()
- Poisson distribution: dpois()
- Student's t distribution: dhyper()
- Uniform distribution: dunif()
- Weibull distribution: dweibull()
