parameters_of_common_distributions

#https://stats.stackexchange.com/questions/302774/does-uniform-distribution-belong-to-location-and-scale-familya
def get_upd_distr(dict_: dict):
    for key, values in dict_.items():
        if key == "norm":
            values[0] = 'mean'
            values[1] = 'sd'
        if key == "cauchy":
            #https://www.itl.nist.gov/div898/handbook/eda/section3/eda3663.htm
            values[0] = 't'       #t
            values[1] = 's'     #s
        if key == 'expon':
            values[0] = 'min value'
            values[1] = '1/lambda'
        if key == "chi2":
            #https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm
            #https://web.ma.utexas.edu/users/mks/M358KInstr/tDistandDF.pdf
            values[0] = 'df' #TODO understand
            values[1] = 'mean'
            values[2] = 'sd'
        if key == "lognorm":
            #https://statisticsbyjim.com/probability/lognormal-distribution/
            #https://stackoverflow.com/questions/8747761/scipy-lognormal-distribution-parameters
            values[0] = 'sd'       #shape
            values[1] = 'mean'     #loc
            values[2] = 'alpha'    #scale
        if key == 'uniform':
            #https://statisticsbyjim.com/probability/gamma-distribution/
            values[0] = 'a'
            values[1] = '|b-a|'
        if key == 'rayleigh':
            #https://anylogic.help/advanced/functions/rayleigh.html
            #https://stats.stackexchange.com/questions/224416/parameter-estimation-of-a-rayleigh-random-variable-with-an-offset --useful
            values[0] = 'mean'
            values[1] = 'sd'
        if key == 'powerlaw':   #TODO understand what is it
            values[0] = 'alpha'
            values[1] = 'Xmin'
            values[2] = 'D' #Kolmogorov smirnov statistic
        if key == 'exponpow':   #TODO understand what is it
            values[0] = 'b'
            values[1] = 'loc'
            values[2] = 'scale'
        if key == 'gamma':
            #https://stackoverflow.com/questions/2896179/fitting-a-gamma-distribution-with-python-scipy
            #https://statisticsbyjim.com/probability/gamma-distribution/
            #https://en.wikipedia.org/wiki/Gamma_distribution
            #https://pythonguides.com/python-scipy-stats-fit/
            values[0] = 'alpha' #shape
            values[1] = 'loc'   #scale
            values[2] = 'betta' #thres
        if key == 'beta':
            # https://stats.stackexchange.com/questions/68983/beta-distribution-fitting-in-scipy
            values[0] = 'alpha'
            values[1] = 'beta'
            values[2] = 'lower limit'
            values[3] = 'upper limit - lower limit'
        if key == 'burr':
            """
            In terms of mathematical statistics, the loc and scale parameters for the Burr distribution correspond to the shift and scale parameters.

            The loc parameter represents a shift (or offset) of the distribution along the axis of values. If loc is a, then the distribution will be shifted by a units to the right (positive value) or to the left (negative value).
            The scale parameter represents the scale that affects the spread of the data. If scale is equal to b, then the distribution will be scaled along the axis of values.
            So you can rewrite the values of loc and scale in terms of mathematical statistics as follows:

            Shift (loc):μ=loc

            Scale (scale):σ=scale

            Here
            μ is the mean (shift), and σ is the standard deviation (scale).
            """
            values[0] = 'c' #tail parameter
            values[1] = 'd'
            values[2] = 'mean'
            values[3] = 'sd'