Showing posts with label Distributions. Show all posts
Showing posts with label Distributions. Show all posts

Probability Distributions (I)

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()