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  5. Determination of relative estimate of the weight of distribution tail area -tail level

Determination of relative estimate of the weight of distribution tail area -tail level

V.Yu. Dubnitskiy, A.I. Khodyrev
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A logarithmic relative measure was introduced for the weight of distribution tail area – tail level. The proposed measure is a function of relation between tail area values of compared and basic (reference) distributions expressed in decibels. It was shown that the proposed measure substantially depends on types of compared distributions, level of compared probability and calculation accuracy. For one-parameter distributions such as exponential distribution, Rayleigh distribution, simplified Rayleigh-Rice distribution, Maxwell distribution, hyperexponential distribution, tail level was determined relative to Pareto distribution. For two-parameter distributions determined on an added semiaxis, such as second type beta distribution, gamma distribution, normalized second order Erlang distribution, Weibull distribution, second order hyperexponential distribution, twodimensional random vector modulus distribution, Nakagami distribution, inverse Gaussian distribution, special form distribution, tail level was determined relative to logarithmic normal distribution. For two-parameter distributions determined on numerical axis, such as Laplace distribution, minimum value distribution, maximum value distribution, tail level was determined relative to normal distribution.
Keywords: distribution tail area, decibels, tail level, exponential distribution, Rayleigh distribution, simplified RayleighRice distribution, Maxwell distribution, hyperexponential distribution, Pareto distribution, second type beta distribution, gamma distribution, normalized second order Erlang distribution, Weibull distribution, second order hyperexponential distribution, twodimensional random vector modulus distribution, Nakagami distribution, inverse Gaussian distribution, special form distribution, logarithmic normal distribution, Laplace distribution, minimum value distribution, maximum value distribution, double exponential distribution, logistic distribution, Champernaum distribution, normal distribution