15:[["$","meta","0",{"name":"viewport","content":"width=device-width, initial-scale=1"}],["$","meta","1",{"charSet":"utf-8"}],["$","title","2",{"children":"lognorm() R function from [VaRES] | R PACKAGES"}],["$","meta","3",{"name":"description","content":"Computes the pdf, cdf, value at risk and expected shortfall for the lognormal distribution given by [REMOVE_ME]$$ \\begin{array}{ll}&\\displaystylef (x) = \\frac {1}{\\sigma x} \\phi \\left( \\frac {\\log x - \\mu}{\\sigma} \\right),\\\\&\\displaystyleF (x) = \\Phi \\left( \\frac {\\log x - \\mu}{\\sigma} \\right),\\\\&\\displaystyle{\\rm VaR}_p (X) = \\exp \\left[ \\mu + \\sigma \\Phi^{-1} (p) \\right],\\\\&\\displaystyle{\\rm ES}_p (X) = \\frac {\\exp (\\mu)}{p} \\int_0^p \\exp \\left[ \\sigma \\Phi^{-1} (v) \\right] dv\\end{array} [REMOVE_ME_2]$$\n\nfor $x > 0$, $0 < p < 1$, $-\\infty < \\mu < \\infty$, the location parameter, and $\\sigma > 0$, the scale parameter."}],["$","meta","4",{"property":"og:title","content":"lognorm() R function from [VaRES]"}],["$","meta","5",{"property":"og:description","content":"Computes the pdf, cdf, value at risk and expected shortfall for the lognormal distribution given by [REMOVE_ME]$$ \\begin{array}{ll}&\\displaystylef (x) = \\frac {1}{\\sigma x} \\phi \\left( \\frac {\\log x - \\mu}{\\sigma} \\right),\\\\&\\displaystyleF (x) = \\Phi \\left( \\frac {\\log x - \\mu}{\\sigma} \\right),\\\\&\\displaystyle{\\rm VaR}_p (X) = \\exp \\left[ \\mu + \\sigma \\Phi^{-1} (p) \\right],\\\\&\\displaystyle{\\rm ES}_p (X) = \\frac {\\exp (\\mu)}{p} \\int_0^p \\exp \\left[ \\sigma \\Phi^{-1} (v) \\right] dv\\end{array} [REMOVE_ME_2]$$\n\nfor $x > 0$, $0 < p < 1$, $-\\infty < \\mu < \\infty$, the location parameter, and $\\sigma > 0$, the scale parameter."}],["$","meta","6",{"property":"og:url","content":"https://r-packages.io/packages/VaRES/lognorm"}],["$","meta","7",{"property":"og:site_name","content":"R PACKAGES"}],["$","meta","8",{"property":"og:locale","content":"en_US"}],["$","meta","9",{"property":"og:image:type","content":"image/png"}],["$","meta","10",{"property":"og:image","content":"https://r-packages.io/packages/VaRES/lognorm/opengraph-image?6cdc95b0c38aa621"}],["$","meta","11",{"property":"og:image:width","content":"1200"}],["$","meta","12",{"property":"og:image:height","content":"630"}],["$","meta","13",{"property":"og:type","content":"website"}],["$","meta","14",{"name":"twitter:card","content":"summary_large_image"}],["$","meta","15",{"name":"twitter:title","content":"lognorm() R function from [VaRES]"}],["$","meta","16",{"name":"twitter:description","content":"Computes the pdf, cdf, value at risk and expected shortfall for the lognormal distribution given by [REMOVE_ME]$$ \\begin{array}{ll}&\\displaystylef (x) = \\frac {1}{\\sigma x} \\phi \\left( \\frac {\\log x - \\mu}{\\sigma} \\right),\\\\&\\displaystyleF (x) = \\Phi \\left( \\frac {\\log x - \\mu}{\\sigma} \\right),\\\\&\\displaystyle{\\rm VaR}_p (X) = \\exp \\left[ \\mu + \\sigma \\Phi^{-1} (p) \\right],\\\\&\\displaystyle{\\rm ES}_p (X) = \\frac {\\exp (\\mu)}{p} \\int_0^p \\exp \\left[ \\sigma \\Phi^{-1} (v) \\right] dv\\end{array} [REMOVE_ME_2]$$\n\nfor $x > 0$, $0 < p < 1$, $-\\infty < \\mu < \\infty$, the location parameter, and $\\sigma > 0$, the scale parameter."}],["$","meta","17",{"name":"twitter:image:type","content":"image/png"}],["$","meta","18",{"name":"twitter:image","content":"https://r-packages.io/packages/VaRES/lognorm/opengraph-image?6cdc95b0c38aa621"}],["$","meta","19",{"name":"twitter:image:width","content":"1200"}],["$","meta","20",{"name":"twitter:image:height","content":"630"}],["$","link","21",{"rel":"icon","href":"/favicon.ico","type":"image/x-icon","sizes":"16x16"}],["$","meta","22",{"name":"next-size-adjust"}]]

lognorm function