Probablity ditributions

Discrete distributions

Binomial

The R root name is binom.

Geometric

The R root name is geom.

Hypergeometric

The R root name is hyper.

Negative binomial

The R root name is nbinom.

Poisson

The R root name is pois.

Continuous distributions

Beta

The R root name is beta.

Cauchy

The R root name is cauchy.

Chi-squared

The chi-square distribution is a special case of the gamma distribution.

It is a widely used distributions in inferential statistics, primarily in hypothesis testing or in construction of confidence intervals because of its (mathematical) relationship to the normal distribution.

The R root name is chisq.

help Chisquare

Exponential

The R root name is exp.

F

The R root name is f.

Gamma

The R root name is gamma.

Log-normal

The R root name is lnorm.

help Lognormal

Logistic

The R root name is logis.

Normal

The normal distribution is a measure of location, rather than goodness-of-fit.

A normal distribution has zero kurtosis.

The R root name is norm.

Student's t

The R root name is t.

R: help TDist

Uniform

The R root name is unif.

Weibull

The R root name is weibull.

Wilcoxon

The R root name is wilcox.

Terminology

Mode: the value with highest probability for discrete variables, a location at which the probability density function has a local peak for continuous variables
Frequency: The number of times a certain variable apperas
Support: the smallest closed set whose complement has probability zero.
Head: the range of values where the pmf or pdf is (relatively) high. Tail is the head's complement within the support.
Mean: The weighted average of possible values. The weights are the values' probabilities. Aka: expected value.
Range: The difference between the lowest and highest value.
Variance: The second moment of the pmf or pdf about the mean. It measures the dispersion of the distribution.
Standard deviation (σ): the second moment of the pmf or pdf about the mean. Another measure of dispersion. The standard deviation measures how close the data is centered around the mean.
Symmetry: a property of some distributions in which the portion of the distribution to the left of a specific value is a mirror image of the portion to its right.
Skewness: a measure of the extent to which a pmf or pdf "leans" to one side of its mean.
Kurtosis: a measure of the "fatness" of the tails of a pmf or pdf. The fourth standardized moment of the distribution.
Median: Half of data points below, other half above.

Cumulative distribution function (CDF)

Cumulative distribution function, aka cumulative densitiy function is the probability that a random variable, evaluated at x, is less than or equal to x.

In R, The CDFs of probability distribution can be calculated with the p prefix.