if (v <= 0) { return undefined; }
var dfs = {
mean: function () {
if (v > 1) {
return 0;
} else {
return undefined;
}
}(),
median: 0,
mode: 0,
variance: function () {
if (v > 2) {
return v / (v - 2);
} else {
if (v > 1) {
return Infinity;
} else {
return undefined;
}
}
}(),
skewness: function () {
if ( v > 3) {
return 0;
} else {
return undefined;
}
}(),
entropy: 'to be implemented', // @todo: circle back and implement this after implementing digamma and beta functions.
domain: { min: -Infinity, max: Infinity },
range: { min: 0, max: Infinity },
pdf: function (x) {
return (mctad.Γ((v + 1) / 2) / (Math.sqrt(v * mctad.π) * mctad.Γ(v / 2)) * Math.pow((1 + Math.pow(x, 2) / v), -((v + 1) / 2)));
},
cdf: function (x) {
var cdf = [];
for (var key in mctad.t_distribution_table[v]) {
cdf.push([parseFloat(key), parseFloat(mctad.t_distribution_table[v][key])]);
cdf.push([parseFloat(1.0 - key), parseFloat(-mctad.t_distribution_table[v][key])]);
}
cdf.sort(function (a, b) {
return a[1] - b[1];
});
var i = 0;
while (cdf[i][1] < x) {
i++;
}
return cdf[i][0];
}
};
Student's t-Distribution
The Student's t-Distribution
Assumptions
v, the degrees of freedom, is a strictly positive real number.Use
mctad.studentsT(v)Inline Comments