A probability distribution is characterized by scale as its parameter. Whenever the scale is large the more spread out the distribution will be and whenever the scale is small it will be more concentrated.

hist(rlogis(4000, 0, scale = 5))

hist(rlogis(4000, 0, scale = 500))

The shape of a distribution is used in finding the appropriate shape of a statistical model of a population. Skewness and Kurtosis are concepts encompassing the shape of the distribution.

hist(rbeta(10000,5,2))

hist(rbeta(10000,2,5))

hist(rbeta(10000,5,5))