An alternative inverse Gaussian distribution expressed in terms of the Bessel function is introduced. Both theoretical and empirical motivation is provided. Various particular cases and expressions for moments are derived. Estimation procedures by the method of moments and the method of maximum...

Gamma distributions are some of the most popular models for hydrological processes. In this paper, a very flexible family which contains the gamma distribution as a particular case is introduced. Evidence of flexibility is shown by examining the shape of its probability density function (pdf). A...

Soltani and Shirvani (Comput Stat 25:155–161, <CitationRef CitationID="CR10">2010</CitationRef>) proposed a scheme for simulating truncated stable random variables. That involves solving a nonlinear transformation in each realization. Here, we propose alternative schemes to generate truncated stable random variables. Our schemes are more...</citationref>

Given a random sample of size <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$n$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>n</mi> </math> </EquationSource> </InlineEquation> with mean <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\overline{X} $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mover> <mi>X</mi> <mo>¯</mo> </mover> </math> </EquationSource> </InlineEquation> and standard deviation <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$s$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>s</mi> </math> </EquationSource> </InlineEquation> from a symmetric distribution <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$F(x; \mu , \sigma )=F_{0} (( x- \mu ) / \sigma ) $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>F</mi> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo>;</mo> <mi mathvariant="italic">μ</mi> <mo>,</mo> <mi mathvariant="italic">σ</mi> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <msub> <mi>F</mi> <mn>0</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo>-</mo> <mi mathvariant="italic">μ</mi> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">/</mo> <mi mathvariant="italic">σ</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math> </EquationSource> </InlineEquation> with <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$F_0$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>F</mi> <mn>0</mn> </msub> </math> </EquationSource> </InlineEquation>...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

The novel Balakrishnan skew-normal distribution was introduced in 2008. The only known scheme for simulating from this distribution is based on acceptance/rejection sampling. Here, we introduce an alternative scheme that is more efficient. We also derive various stochastic representations for...

Most of the financial institutions compute the Value-at-Risk (VaR) of their trading portfolios using historical simulation-based methods. In this paper, we examine the Filtered Historical Simulation (FHS) model introduced by Barone-Adesi et al. (1999) theoretically and empirically. The main goal...