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In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then Y = ln( X ) has a normal distribution.
In probability theory, a logit-normal distribution is a probability distribution of a random variable whose logit has a normal distribution.If Y is a random variable with a normal distribution, and t is the standard logistic function, then X = t(Y) has a logit-normal distribution; likewise, if X is logit-normally distributed, then Y = logit(X)= log (X/(1-X)) is normally distributed.
Conversely, if X is a lognormal (μ, σ 2) random variable then log X is a normal (μ, σ 2) random variable. If X is an exponential random variable with mean β, then X 1/γ is a Weibull (γ, β) random variable. The square of a standard normal random variable has a chi-squared distribution with one degree of freedom.
The normal distribution, also called the Gaussian or the bell curve. It is ubiquitous in nature and statistics due to the central limit theorem: every variable that can be modelled as a sum of many small independent, identically distributed variables with finite mean and variance is approximately normal. The normal-exponential-gamma distribution
Since probability tables cannot be printed for every normal distribution, as there are an infinite variety of normal distributions, it is common practice to convert a normal to a standard normal (known as a z-score) and then use the standard normal table to find probabilities. [2]
Survival functions that are defined by parameters are said to be parametric. In the four survival function graphs shown above, the shape of the survival function is defined by a particular probability distribution: survival function 1 is defined by an exponential distribution, 2 is defined by a Weibull distribution, 3 is defined by a log ...
The simplest case of a normal distribution is known as the standard normal distribution or unit normal distribution. This is a special case when μ = 0 {\textstyle \mu =0} and σ 2 = 1 {\textstyle \sigma ^{2}=1} , and it is described by this probability density function (or density): φ ( z ) = e − z 2 2 2 π . {\displaystyle \varphi (z ...
Normal probability plots are made of raw data, residuals from model fits, and estimated parameters. A normal probability plot. In a normal probability plot (also called a "normal plot"), the sorted data are plotted vs. values selected to make the resulting image look close to a straight line if the data are approximately normally distributed.