Mixture of Normal Distributions Body Mass Indices Among

Mixture of Normal Distributions Body Mass Indices Among NBA, WNBA, EPL, and NHL Athletes

Data • Body Mass Indices (BMI) Among Professional Athletes in 4 Leagues § § NBA (2013 -14) – N 1 = 505, m 1 = 24. 74, s 1 = 1. 72 WNBA (2014) – N 2 = 139, m 2 = 23. 14, s 2 = 2. 10 EPL (2015) – N 3 = 526, m 3 = 23. 02, s 3 = 1. 71 NHL (2014 -15) – N 4 = 717, m 4 = 26. 50, s 4 = 1. 45 • Distributions are approximately Normal • Weights (proportions of players by league): § p 1 = 0. 2676 p 2 = 0. 0737 p 3 = 0. 2787 p 4 = 0. 3800

WNBA BMI Distribution 45 20 40 18 35 16 30 14 25 12 20 10 15 8 10 6 5 4 0 2 20 20, 5 21 21, 5 22 22, 5 23 23, 5 24 24, 5 25 25, 5 26 26, 5 27 27, 5 28 28, 5 29 29, 5 30 30, 5 31 BMI 0 16, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 5 EPL BMI Distribution 50 NHL BMI Distribution 80 45 70 40 60 35 30 50 25 40 20 30 15 Count 20 10 10 5 0 18 18, 5 19 19, 5 20 20, 5 21 21, 5 22 22, 5 23 23, 5 24 24, 5 25 25, 5 26 26, 5 27 27, 5 28 28, 5 29 29, 5 30 30, 5 31 0 21 21, 5 22 22, 5 23 23, 5 24 24, 5 25 25, 5 26 26, 5 27 27, 5 28 28, 5 29 29, 5 30 30, 5 31 31, 5 32 Frequncy NBA BMI Distribution

Body Mass Index Distributions by Sports League 0, 3 0, 25 Normal Density 0, 2 NBA 0, 15 NHL EPL WNBA 0, 1 0, 05 0 16 18 20 22 24 BMI 26 28 30 32

Mixture of Normal Distributions

Sports League Model for BMI Obtained using =average(a 2: a 1888) =var. p(a 2: a 1888)

Mixture of Normals - True Weights 0, 18 0, 16 0, 14 0, 12 0, 1 0, 08 0, 06 0, 04 0, 02 0 16 18 20 22 24 26 28 30 32