Normal and Student´s t Distributions and Their Applications

Diurnal Variability Of Underwater Acoustic Noise Characteristics in Shallow Water

“…The lower the value of , wider the tails of the pdf becomes and vice versa. The general Student's t distribution has the following properties [17]: a) It has mean = 0 and the standard deviation is greater 1 for degrees of freedom, greater than 2 and it does not exist for 1 and 2 degrees of freedom. For sufficiently large values of the degree of freedom, the Student pdf converges to the Gaussian distribution.…”

Likelihood-based inference for the power half-normal distribution

“…Then one obtains, as a particular case, the Shannon entropy for the half-normal distribution (see Ahsanullah et al 2014), which is given by…”

Characterizations of continuous probability distributions occurring in physics and allied sciences by truncated moment

“…For details on some of these distributions, the interested readers are referred to Johnson et al [10], [11], Evans et al [4], Balakrishnan and Nevzorov [3], and Ahsanullah, et al [2], among others. As pointed out by Oldham, et al [14], normal, logistic, and Lorentz (also known as the Cauchy) distributions have applications in chemical separation process, where the chromatographic peaks follow a normal distribution, and the electrochemical peaks follow a logistic distribution.…”

“…Before a particular probability distribution model is applied to fit the real-world data, it is necessary to confirm whether the given continuous probability distribution satisfies the underlying requirements by its characterization. A probability distribution can be characterized through various methods, see, for example, Ahsanullah et al [2], among others. In recent years, there has been a great interest in the characterizations of probability distributions by truncated moments.…”