8a76faaa-1e52-40ed-96e4-fcc4ef3d96a2 22 4 5 false false 0 decimal

&[DATE] &[TIME] - &[FILENAME]

underlying data

x 709011013015018022527532591 mat :

y 0.0024 0.0056 0.0051 0.00545 0.00565 0.00455 0.00302 0.00152 0.0019 91 mat :

x g1 70 0.0024 90 0.0056 110 0.0051 130 0.00545 150 0.00565 180 0.00455 225 0.00302 275 0.00152 325 0.0019 92 mat :

x g1

we introduce a formula for the approximation

a1 1002 π * sqrt * :

Wb h1 σ1 a1 * / (x μ1 - (2^2 σ1 2^* / - exp * h2 σ2 a1 * / (x μ2 - (2^- 2 σ2 2^* / exp * + h3 σ3 a1 * / (x μ3 - (2^- 2 σ3 2^* / exp * + :

initial values of 9 parameters

10 parameters that need to be calculated, we set arbitrary values for now

h1 0 :

h2 0 :

h3 0 :

μ1 50 :

μ2 100 :

μ3 200 :

Sqmin 1 :

hh1 0.15 :

hh2 0.7 :

hh3 0.40 :

σ1 1 :

σ2 1 :

σ3 1 :

μμ1 90 :

μμ2 160 :

μμ3 350 :

σσ1 19 :

σσ2 50 :

σσ3 80 :

The difference between the original data and those calculated by the formula

h1 h2 h3 μ1 μ2 μ3 σ1 σ2 σ3 Raz y Wb - :

the sum of the squares of the deviations of the initial data from the desired function

h1 h2 h3 μ1 μ2 μ3 σ1 σ2 σ3 Sq h1 h2 h3 μ1 μ2 μ3 σ1 σ2 σ3 Raz 2^vectorize (sum :

we iterate through the parameters to minimize the sum of the squared deviations

h1 100 < h1 h1 1 + : h2 100 < h2 h2 1 + : h3 100 < h3 h3 1 + : μ1 200 < μ1 μ1 1 + : μ2 350 < μ2 μ2 1 + : μ3 500 < μ3 μ3 1 + : σ1 80 < σ1 σ1 1 + : σ2 100 < σ2 σ2 1 + : σ3 150 < σ3 σ3 1 + : Sq h1 h2 h3 μ1 μ2 μ3 σ1 σ2 σ3 Sq : Sq Sqmin < hh1 h1 100 / : hh2 h2 100 / : hh3 h3 100 / : μμ1 μ1 : μμ2 μ2 : μμ3 μ3 : σσ1 σ1 : σσ2 σ2 : σσ3 σ3 : Sqmin Sq : 101 line continue if 31 line while 21 line while 21 line while 21 line while 21 line while 21 line while 21 line while 21 line while 21 line while

Here in the loop, Sq should be calculated and compared with Sqmin. The parameters under which the condition is met are saved

Here the program should print the value of the smallest square of the deviation and the values of the 9 parameters at which this is achieved

Sqmin 0.0002

hh1 0.01

hh2 0.01

hh3 0.01

μμ1 51

μμ2 101

μμ3 201

σσ1 2

σσ2 2

σσ3 62

x wh1 hh1 σσ1 2 π * sqrt * / x μμ1 - (2^2 σσ1 2^* / - exp * :

Draw the resulting graphs.
Three normal distributions and their sum with different weights

x wh2 hh2 σσ2 2 π * sqrt * / x μμ2 - (2^2 σσ2 2^* / - exp * :

x wh3 hh3 σσ3 2 π * sqrt * / x μμ3 - (2^2 σσ3 2^* / - exp * :

x WW x wh1 x wh2 + x wh3 + :

x g1 x WW x wh1 x wh2 x wh3 5 1 sys