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...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

A microgrid energy management framework for the optimization of individual objectives of microgrid stakeholders is proposed. The framework is exemplified by way of a microgrid that is connected to an external grid via a transformer and includes the following players: a middle-size train station...