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(Basic Statistics for Citizen Data Scientist) Distribution Property Functions In the descriptions of the distributions described throughout the website, we have provided formulas for the distribution mean and variance. Real Statistics provides the following functions to carry out these calculations. Real Statistics Functions: The Real Statistics Resource Pack contains the following functions. MEAN_DIST(dist, param1, param2, …

(Basic Statistics for Citizen Data Scientist) Laplace Distribution The pdf of the Laplace distribution (aka the double exponential distribution) with location parameter μ and scale parameter β is where β > 0. The cdf is The inverse of the Laplace distribution is Key statistical properties of the Laplace distribution are shown in Figure 1. Figure 1 – Statistical properties of …

(Basic Statistics for Citizen Data Scientist) Gumbel Distribution The Gumbel distribution is used to model the largest value from a relatively large set of independent elements from distributions whose tails decay relatively fast, such as a normal or exponential distribution. As a result, it can be used to analyze annual maximum daily rainfall volumes. In …

(Basic Statistics for Citizen Data Scientist) Logistic Distribution The pdf of the Logistic distribution at location parameter µ and scale parameter β is where β > 0. The cdf is The inverse of the logistic distribution is The standard Gumbel distribution is the case where μ = 0 and β = 1. Key statistical properties of the Logistic distribution are shown in Figure 1. …

(Basic Statistics for Citizen Data Scientist) Weibull Distribution Definition 1: The Weibull distribution has the probability density function (pdf) for x ≥ 0. Here β > 0 is the shape parameter and α > 0 is the scale parameter. The cumulative distribution function (cdf) is The inverse cumulative distribution function is I(p) = Observation: There is also a three-parameter version of the Weibull distribution. Observation: If x represents “time-to-failure”, the …

(Basic Statistics for Citizen Data Scientist) Uniform Distribution When you ask for a random set of say 100 numbers between 1 and 10, you are looking for a sample from a continuous uniform distribution, where α = 1 and β = 10 according to the following definition. Definition 1: The continuous uniform distribution has probability density function (pdf) given by where α and β are any parameters …

(Basic Statistics for Citizen Data Scientist) Exponential Distribution The exponential distribution can be used to determine the probability that it will take a given number of trials to arrive at the first success in a Poisson distribution; i.e. it describes the inter-arrival times in a Poisson process. It is the continuous counterpart to the geometric distribution, and …