Explanation: Two important methods in the analysis is differentiation and Fourier transformation. Unfortunately, not all functions are differentiable or have a Fourier transform.

Explanation: Every continuous random variable x has a great Probability Density Function (PDF). The PDF can sometimes be greater than 1. This is in contrast to the discrete case.

Explanation: distrEx provides some extensions of package distr and further functionalities like var, sd, IQR, mad, median, skewness, kurtosis truncated moments.

Explanation: When µ = 0 and σ = 1 we say that the random variable has a standard normal distribution and we typically write Z ∼ norm(mean = 0, sd = 1).

Explanation: The lowercase Greek letter phi (φ) is used to denote the standard normal PDF and the capital Greek letter phi Φ is used to denote the standard normal CDF.

Explanation: The distr package has a functionality to find the transformations of one variable distribution. There are exact results for the ordinary transformations for the standard distributions, and distr takes advantage of these in many cases.

Explanation: The Cauchy distribution looks like a norm distribution but with very heavy tails. The mean (and variance) do not exist, that is, they are infinite.

Explanation: The median is represented by the location parameter, and the scale parameter influences the spread of the distribution about its median.

Explanation: The scale parameter influences the spread of the distribution about its median. The median is represented by the location parameter.

Explanation: Beta distribution comes up a lot in Bayesian statistics because it is a good model for one’s prior beliefs about a population proportion.

Explanation: The associated R function is dlogis (x, location = 0, scale = 1). The logistic distribution comes up in differential equations as a model for population growth under certain assumptions.

Explanation: The associated R function is dlogis(x, location = 0, scale = 1). The logistic distribution comes up in differential equations as a model for population growth under certain assumptions.

Explanation: Lognormal distribution is a distribution derived from the normal distribution (hence the name). Its name also says that it is derived from the normal distribution.

Explanation: The associated R function is dlnorm(x, meanlog = 0, sdlog = 1). Lognormal distribution is a distribution derived from the normal distribution (hence the name). Its name also says that it is derived from the normal distribution.

Explanation: The associated R function is dweibull(x, shape, scale = 1). There are exact results for ordinary transformations of the standard distributions, and distr takes advantage of these in many cases.