The distribution of the quotient of two triangularly distributed random variables
The exact distributions of the quotients <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$X/Y$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>X</mi> <mo stretchy="false">/</mo> <mi>Y</mi> </mrow> </math> </EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$Y/(X+Y)$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>Y</mi> <mo stretchy="false">/</mo> <mo stretchy="false">(</mo> <mi>X</mi> <mo>+</mo> <mi>Y</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation> when <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$X$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>X</mi> </math> </EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$Y$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>Y</mi> </math> </EquationSource> </InlineEquation> are independent and triangularly distributed random variables are obtained. These quotients are useful especially in operations research and reliability engineering, and some reliability applications of the results are also given. Copyright Springer-Verlag Berlin Heidelberg 2015
