The Estimation of Distribution Function of Rohrer-Index at Each Level of Height.

Abstract

Rohrer-Index is commonly used to measure the level of fatness and thinness of body with numerical expression, (<weight (g)>/<height (cm)>) X 100^2. In the present study the distribution of Rohrer-Index at each level of height is considered by conditional probability theory. Distribution function of Rohrer-Index (X/y^3=u)^* under Condition y is f(u|y)= ((1/(√<2π(σ_1/y^3)√<1-ρ^2>)e-1/(2σ_1^2(1-ρ^2)/y^6))(u-1/y^3(μ_1+(<ρσ_1>/σ_2)(y-μ_2)))^2(cf.Eq.(15)) The expectation of Rohrer-Index at each level of height is estimated to be E(u|y)= (1/y^3)(μ_1+(<ρσ_1>/σ_2)(y-μ_2)). (It is named COP function of Rohrer-Index). The standard deviation of Rohrer-Index at each level of height is (σ_1√<1-ρ^2>/y^3. Two examples of data analysis are illustrated. Among eight years old boys the expectation of Rohrer-Index is the higher, the lower the height of boys is, and the expectation is the lower, the higher the height is. Among eleven years old girls the expectation of Rohrer-Index is highest near the mean height, while the higher and the lower girls have the lower expectation of Rohrer-Index. This relationship is similar to inverted U curve.