Motivated by hydrological problems, the exact distributions of the sum X + Y, the product X Y and the ratio X/(X + Y) are derived when X and Y are independent Pareto random variables. A detailed application of the results is provided to extreme rainfall data from Florida. Copyright...

The Pareto classical distribution is one of the most attractive in statistics and particularly in the scenario of actuarial statistics and finance. For example, it is widely used when calculating reinsurance premiums. In the last years, many alternative distributions have been proposed to obtain...

The Pareto classical distribution is one of the most attractive in statistics and particularly in the scenario of actuarial statistics and finance. For example, it is widely used when calculating reinsurance premiums. In the last years, many alternative distributions have been proposed to obtain...

We consider a problem of characterization of continuous distributions for which linearity of regression of overlapping order statistics, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\mathbb {E}(X_{i:m}|X_{j:n})=aX_{j:n}+b$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi mathvariant="double-struck">E</mi> <mrow> <mo stretchy="false">(</mo> <msub> <mi>X</mi> <mrow> <mi>i</mi> <mo>:</mo> <mi>m</mi> </mrow> </msub> <mo stretchy="false">|</mo> <msub> <mi>X</mi> <mrow> <mi>j</mi> <mo>:</mo> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mi>a</mi> <msub> <mi>X</mi> <mrow> <mi>j</mi> <mo>:</mo> <mi>n</mi> </mrow> </msub> <mo>+</mo> <mi>b</mi> </mrow> </math> </EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$m\le n$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>m</mi> <mo>≤</mo> <mi>n</mi> </mrow> </math> </EquationSource> </InlineEquation>, holds. Due to a new...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

Bivariate gamma distributions have been used successfully on modeling hydrological processes. In this work, supposing that X and Y follow the Crovelli’s bivariate gamma model, we deduce the exact distributions of the functions U = X + Y, P = XY and Q = X/(X + Y), as well as...