klesstilne1

2022-11-18

Estimating Gaussian parameters of a set of data points

I have a set of data points. When I draw a histogram of them, plotting their frequency of occurrence against them, I get a curve that looks like a normal curve. I am also able to perform test on the data set to know whether it follows a normal distribution or more precisely whether the population it comes from follows a normal probability distribution. I am using Shapiro Wilk test for it.

However, how can I know what the equation of that normal curve will be? Moreover, is there a way I can test whether other standard distributions fit the points more accurately, and estimate their parameters?

I have a set of data points. When I draw a histogram of them, plotting their frequency of occurrence against them, I get a curve that looks like a normal curve. I am also able to perform test on the data set to know whether it follows a normal distribution or more precisely whether the population it comes from follows a normal probability distribution. I am using Shapiro Wilk test for it.

However, how can I know what the equation of that normal curve will be? Moreover, is there a way I can test whether other standard distributions fit the points more accurately, and estimate their parameters?

metodikkf6z

Beginner2022-11-19Added 14 answers

Step 1

You can estimate the parameters $\mu $ and $\sigma $ by using the statistics:

$\hat{\mu}=\overline{X}=\frac{1}{n}\sum {X}_{i}$

and

${\hat{\sigma}}^{2}=\frac{1}{n-1}\sum ({X}_{i}-\overline{X}{)}^{2}$

Step 2

Where ${X}_{i}$ would be the ith sample element. Thus $\overline{X}$ is the sample mean. So the equation of the fitted distribution would be:

$f(x)={\displaystyle \frac{1}{\sqrt{2\pi {\hat{\sigma}}^{2}}}}{e}^{-{\displaystyle \frac{(x-\hat{\mu}{)}^{2}}{2{\hat{\sigma}}^{2}}}}$

You can use the Pearson Chi Squared test to check the hypothesis that the data comes from the distribution being tested.

You can estimate the parameters $\mu $ and $\sigma $ by using the statistics:

$\hat{\mu}=\overline{X}=\frac{1}{n}\sum {X}_{i}$

and

${\hat{\sigma}}^{2}=\frac{1}{n-1}\sum ({X}_{i}-\overline{X}{)}^{2}$

Step 2

Where ${X}_{i}$ would be the ith sample element. Thus $\overline{X}$ is the sample mean. So the equation of the fitted distribution would be:

$f(x)={\displaystyle \frac{1}{\sqrt{2\pi {\hat{\sigma}}^{2}}}}{e}^{-{\displaystyle \frac{(x-\hat{\mu}{)}^{2}}{2{\hat{\sigma}}^{2}}}}$

You can use the Pearson Chi Squared test to check the hypothesis that the data comes from the distribution being tested.

The product of the ages, in years, of three (3) teenagers os 4590. None of the have the sane age. What are the ages of the teenagers???

Use the row of numbers shown below to generate 12 random numbers between 01 and 99

78038 18022 84755 23146 12720 70910 49732 79606

Starting at the beginning of the row, what are the first 12 numbers between 01 and 99 in the sample?How many different 10 letter words (real or imaginary) can be formed from the following letters

H,T,G,B,X,X,T,L,N,J.Is every straight line the graph of a function?

For the 1s orbital of the Hydrogen atom, the radial wave function is given as: $R(r)=\frac{1}{\sqrt{\pi}}(\frac{1}{{a}_{O}}{)}^{\frac{3}{2}}{e}^{\frac{-r}{{a}_{O}}}$ (Where ${a}_{O}=0.529$ ∘A)

The ratio of radial probability density of finding an electron at $r={a}_{O}$ to the radial probability density of finding an electron at the nucleus is given as ($x.{e}^{-y}$). Calculate the value of (x+y).Find the sets $A$ and $B$ if $\frac{A}{B}=\left(1,5,7,8\right),\frac{B}{A}=\left(2,10\right)$ and $A\cap B=\left(3,6,9\right)$. Are they unique?

What are the characteristics of a good hypothesis?

If x is 60% of y, find $\frac{x}{y-x}$.

A)$\frac{1}{2}$

B)$\frac{3}{2}$

C)$\frac{7}{2}$

D)$\frac{5}{2}$The numbers of significant figures in $9.1\times {10}^{-31}kg$ are:

A)Two

B)Three

C)Ten

D)Thirty oneWhat is positive acceleration?

Is power scalar or vector?

What is the five-step process for hypothesis testing?

How to calculate Type 1 error and Type 2 error probabilities?

How long will it take to drive 450 km if you are driving at a speed of 50 km per hour?

1) 9 Hours

2) 3.5 Hours

3) 6 Hours

4) 12.5 HoursWhat is the square root of 106?