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Yes. Think of a function that starts at the origin, increases rapidly at first and then decays gradually to an asymptotic value of 0. It will have attained its asymptotic value at the start. For example, the Fisher F distribution, which is often used, in statistics, to test the significance of regression coefficients. Follow the link for more on the F distribution.
It means that the probability distribution function of the variable is the Gaussian or normal distribution.
By standard practice, the normal distribution curve should be normalized so that the area under the curve is 1. This results in a height, at the mean, of about 0.4, i.e. the probability of a sample value being equal to the mean is 40 percent. The width of the normal distribution curve is infinite, as the tails are asymptotic to the X axis. It is easier to understand that the +/- one sigma area is 68.2 percent, the +/- two sigma area is 95.4 percent, and the +/- three sigma area is 99.6 percent.
In mathematics, an asymptotic analysis is a method of describing limiting behaviour. The methodology has applications across science such as the analysis of algorithms.
The exponential distribution and the Poisson distribution.