In this Python tutorial, we will learn about the “Python Scipy Stats Norm” to calculate the different types of normal distribution and how to plot it and cover the following topics. Nội dung chính - What is Norm in Statistics?
- Python Scipy Stats Norm Expect
- Python Scipy Stats Norm Plot
- Python Scipy Stats Norm Parameters
- Python Scipy Stats Norm Cdf
- Python Scipy Stats Norm Interval
- Python Scipy Stats Norm Ppf
- Python Scipy Stats Norm Logpdf
- Python Scipy Stats Norm Logcdf
- Python Scipy Stats Norm Gen
- Python Scipy Stats Norm Gennorm
- Python Scipy Stats Norm Rvs
- Python Scipy Stats Norm Fit
Nội dung chính - What is Norm in
Statistics?
- Python Scipy Stats Norm Expect
- Python Scipy Stats Norm Plot
- Python Scipy Stats Norm Parameters
- Python Scipy Stats Norm Cdf
- Python Scipy Stats Norm Interval
- Python Scipy Stats Norm Ppf
- Python Scipy Stats Norm Logpdf
- Python Scipy Stats Norm Logcdf
- Python Scipy Stats Norm Gen
- Python Scipy Stats Norm Gennorm
- Python Scipy Stats Norm Rvs
- Python Scipy Stats Norm Fit
Nội dung chính
- What is Norm in Statistics?
- Python Scipy Stats Norm Expect
- Python Scipy Stats Norm Plot
- Python Scipy Stats Norm Parameters
- Python Scipy Stats Norm Cdf
- Python Scipy Stats Norm Interval
- Python Scipy Stats Norm Ppf
- Python Scipy Stats Norm Logpdf
- Python Scipy Stats Norm Logcdf
- Python Scipy Stats Norm Gen
- Python Scipy Stats Norm Gennorm
- Python Scipy Stats Norm Rvs
- Python Scipy Stats Norm Fit
Nội dung chính - What is Norm in Statistics?
- Python Scipy Stats Norm Expect
- Python Scipy Stats Norm Plot
- Python Scipy Stats Norm Parameters
- Python Scipy Stats Norm Cdf
- Python Scipy Stats Norm Interval
- Python Scipy Stats Norm Ppf
- Python Scipy Stats Norm Logpdf
- Python Scipy Stats Norm Logcdf
- Python Scipy Stats Norm Gen
- Python Scipy Stats Norm Gennorm
- Python Scipy Stats Norm Rvs
- Python
Scipy Stats Norm Fit
Nội dung chính - What is Norm in Statistics?
- Python Scipy Stats Norm Expect
- Python Scipy Stats Norm Plot
- Python Scipy Stats Norm Parameters
- Python Scipy Stats Norm Cdf
- Python Scipy Stats Norm Interval
- Python Scipy Stats Norm Ppf
- Python Scipy Stats Norm Logpdf
- Python Scipy Stats Norm Logcdf
- Python Scipy Stats Norm Gen
- Python Scipy Stats Norm Gennorm
- Python Scipy Stats
Norm Rvs
- Python Scipy Stats Norm Fit
- What is Norm in Statistics
- Python Scipy Stats Norm Pdf
- Python Scipy Stats Norm Expect
- Python Scipy Stats Norm Plot
- Python Scipy Stats Norm Parameters
- Python Scipy Stats Norm Cdf
- Python Scipy Stats Norm Interval
- Python Scipy Stats Norm Ppf
- Python Scipy Stats Norm Gen
- Python Scipy Stats Norm Logpdf
- Python Scipy Stats Norm Logcdf
- Python Scipy Stats
Norm Gennorm
- Python Scipy Stats Norm Rvs
- Python Scipy Stats Norm Fit
What is Norm in Statistics?Norms are statistical depictions of a population, such as the CBSE math scores of male sixth-graders or the IELTS reading scores of female Emma ninth-graders. The test results of an individual are compared with the statistical representation of the population in a norm-referenced score interpretation. In real life, a
representative sample or group is tested rather than the entire population. A norm for the group or set of norms is provided by this. Standards describe what a certain group should be able to perform, while norms indicate what that population can do. Also, check: Python Scipy Mann Whitneyu The scipy.stats.norm represents the random variable that is normally continuous. It has different kinds of functions for normal distribution like CDF, PDF, median, etc. It has two important
parameters loc for the mean and scale for standard deviation, as we know we control the shape and location of distribution using these parameters. The syntax is given below. scipy.stats.norm.method_name(data,loc,size,moments,scale)
Where parameters are: - data: It is a set of points or values that represent evenly sampled data in the form of array data.
- loc: It is used to specify the mean, by default it is 0.
- moments: It is used to calculate
statistics like standard deviation, kurtosis, and mean.
- scale: It is used to specify the standard deviation, by default it is 1.
The above parameters are the common parameter of all the methods in the object scipy.stats.norm() . The methods are given below. - scipy.stats.norm.cdf(): It is used for the cumulative distribution function.
- scipy.stats.norm.pdf(): It is used for the probability density function.
- scipy.stats.norm.rvs():
To get the random variates.
- scipy.stats.norm.stats(): It is used to get the standard deviation, mean, kurtosis, and skew.
- scipy.stats.norm.logpdf(): It is used to get the log related to the probability density function.
- scipy.stats.norm.logcdf(): It is used to find the log related to the cumulative distribution function.
- scipy.stats.norm.sf(): It is used to get the values of the survival
function.
- scipy.stats.norm.isf(): It is used to get the values of the inverse survival function.
- scipy.stats.norm.logsf(): It is used to find the log related to the survival function.
- scipy.stats.norm.mean(): It is used to find the mean related to the normal distribution.
- scipy.stats.norm.medain(): It is used to find the median related to the normal distribution.
- scipy.stats.norm.var():
It is used to find the variance related to the distribution.
- scipy.stats.norm.std(): It is used to find the standard deviation related to the distribution
Let’s take an example by using one of the methods mentioned above to know how to use the methods with parameters. Import the required libraries using the below code. import numpy as np
import matplotlib.pyplot as plt
from scipy import stats
Create observation data values and calculate the probability density function from these data values with mean = 0 and standard deviation = 1 . observatin_x = np.linspace(-4,4,200)
pdf_norm = stats.norm.pdf(observatin_x,loc=0,scale=1)
Plot
the created distribution using the below code. plt.plot(observatin_x,pdf_norm)
plt.xlabel('x-values')
plt.ylabel('PDF_norm_values')
plt.title("Probability density funciton of normal distribution")
plt.show() Scipy Stats Norm This is how to use the method norm() of python Scipy to compute the different distributions of the norm. Read: Python Scipy Eigenvalues Python Scipy Stats Norm ExpectThe method expect() of Python Scioy that exist in a module scipy.stats.rv_continous uses numerical integration, to determine the expected value of a function about the distribution. According to a distribution dist,
a function’s expected value, f(x), is defined as follows: Here in this section. we will determine the expected value of a function about the norm distribution. The syntax is given below. rv_continuous.expect(func=None, args=(), loc=0, scale=1, lb=None, ub=None, conditional=True)
Where parameters are: - func(callable): Calculating an integral for a function. only accepts one parameter. The identity mapping f(x) = x is the default.
- args(tuple): Distribution’s shape parameters.
- loc(float):
It is the location parameter and by default 0.
- scale(float): It is a scale parameter and by default 1.
- lb,ub(scalar): Integration’s lower and upper bounds.
- conditional(boolean): If true is the case, the integral is rectified using the integration interval’s conditional probability. The function’s expected value, subject to the supplied interval, is the return value. False by default.
The method expect()
returns expect of type float which is the expected value that was calculated. Let’s understand with an example by following the below steps: Import the required libraries or methods using the below python code. from scipy.stats import norm
norm(1).expect(lambda a: 1, lb=0.0, ub=1.0)
The above is close to the following code. norm(1).cdf(1.0) - norm(1).cdf(0.0)
If we specify conditional equal to True , norm(1).expect(lambda a: 1, lb=0.0, ub=1.0, conditional = True)
Because of numerical integration, there is a tiny departure from 1. Python Scipy Stats Norm ExpectThis is how to determine the expected value
of a function about the norm distribution. Read: Python Scipy Stats Mode Python Scipy Stats Norm PlotThe method norm() has two parameters loc and scale that we can use to plot the distribution using the library matplotlib. These parameters are defined in the above subsection “Python Scipy Stats Norm”. So plot the distribution by following the below steps: Import the required libraries or methods using
the below python code. import matplotlib.pyplot as plt
import numpy as np
from scipy.stats import norm
Generate data and define the loc and scale parameters using the below code. x_data = np.linspace(0, 30, 200)
loc_pr = 12
scale_pr = 1.5
Compute the pdf of the norm and plot the distribution using the below code. plt.plot(x_data, norm.pdf(x_data, loc=loc_pr, scale=scale_pr))
plt.show() Python Scipy Stats Norm PlotThis is how to plot the normal distribution using the matplotlib library. Read: Python Scipy Minimize Python Scipy Stats Norm ParametersThe Python Scipy method norm() has four main parameters
data , loc , moments and scale that can be used to control the distribution. Let’s understand with an example by following the below steps: Import the required libraries or methods using the below python code. import matplotlib.pyplot as plt
import numpy as np
from scipy.stats import norm
Generate data and define the loc and scale parameters using the below code. x_data = np.linspace(0, 20, 200)
loc_pr = 10
scale_pr = 1
plt.plot(x_data, norm.pdf(x_data, loc=loc_pr, scale=scale_pr))
plt.show()
Change the loc parameter to some value and keep constant the value of the scale parameter using the below code.
loc_pr = 5
scale_pr = 1
plt.plot(x_data, norm.pdf(x_data, loc=loc_pr, scale=scale_pr))
plt.show() Python Scipy
Stats Norm ParametersWhen we change the log_pr to 5, it shifted the distribution towards the left side as we can see in the output. Python Scipy Stats Norm Parameters ExampleAgain, change the scale_pr to some value and keep constant the value of loc_pr using the below code. loc_pr = 5
scale_pr = 3
plt.plot(x_data, norm.pdf(x_data, loc=loc_pr, scale=scale_pr))
plt.show()
When we change the scale_pr to 3, it changes the distribution shape as we can see in the output. Python Scipy Stats Norm Parameters tutorialWe have other parameters of the method norm() that we
can use to get more control over the distribution. This is how to use the parameters of the method norm() of Python Scipy. Read: Python Scipy Normal Test Python Scipy Stats Norm CdfThe object norm() has a method cdf() that calculates the cumulative distribution of the norm. The syntax is given below. scipy.stats.norm.cdf(x,loc,size,scale)
Where parameters are: - x: It is a set of points or values that
represent evenly sampled data in the form of array data.
- loc: It is used to specify the mean, by default it is 0.
- scale: It is used to determine the standard deviation, by default it is 1.
The above parameters are the standard parameter of all the methods in the object scipy.stats.norm() . The methods are given below. Let’s take an example by using one of the methods mentioned above to know how to use the methods with parameters. Import
the required libraries using the below code. import numpy as np
import matplotlib.pyplot as plt
from scipy import stats
Create observation data values and calculate the cumulative distribution from these data values with mean = 0 and standard deviation = 1 . observatin_x = np.linspace(-2,2,200)
cdf_norm = stats.norm.cdf(observatin_x,loc=0,scale=1)
Plot the created distribution using the below code. plt.plot(observatin_x,cdf_norm)
plt.xlabel('x-values')
plt.ylabel('cdf_norm_values')
plt.title("Probability density funciton of normal distribution")
plt.show() Python Scipy Stats Norm CdfThis is how to calculate the cumulative distribution of norm using the method norm.cdf() of Python Scipy. Read: Python Scipy Confidence Interval Python Scipy Stats Norm Interval
The method norm.interval() of Python Scipy computes the endpoints of the distribution’s fractional alpha range, between 0 and 1. The syntax is given below. scipy.stats.interval(alpha, loc=0, scale=1)
Where parameters are: - alpha(float): It is the alpha value.
- loc: It is used to specify the mean, by default it is 0.
- scale: It is used to determine the standard deviation, by default it is 1.
Let’s take an example by following the below
steps: Import the required libraries or methods using the python code. from scipy.stats import norm
Define the alpha value and compute the endpoints of the distribution using the below code. alpha = 0.1
norm.interval(alpha) Python Scipy Stats Norm IntervalThis is how to compute the endpoints of the distribution’s fractional alpha range, between 0 and 1 using the method nomr.interval() of Python Scipy, Python Scipy Stats Norm PpfThe object norm() has a method
ppf() that calculate the Percent point function of the norm. In other words, The method norm. ppf() accepts a percentage and returns a standard deviation multiplier for the value that percentage occurs at. The syntax is given below. scipy.stats.norm.ppf(q,loc,size,scale)
Where parameters are: - q: It is a percentage.
- loc: It is used to specify the mean, by default it is 0.
- scale: It is used to determine the standard deviation, by default it is
1.
Let’s understand with an example by following the below code. from scipy.stats import norm
norm.ppf(0.99, loc=0, scale=1)
The above code gives a one-tail test result with a 99% confidence interval for a normal distribution. Python Scipy Stats Norm PpfRead: Scipy Find Peaks This is how to compute a standard deviation multiplier for the value using the method norm.ppf() of Python Scipy. Python Scipy Stats Norm LogpdfThe object norm() has a method logpdf()
that calculates the log probability of the norm. The syntax is given below. scipy.stats.norm.logpdf(x,loc,size,scale)
Where parameters are: - x: It is a set of points or values that represent evenly sampled data in the form of array data.
- loc: It is used to specify the mean, by default it is 0.
- scale: It is used to determine the standard deviation, by default it is 1.
The above parameters are the standard parameter of all the
methods in the object scipy.stats.norm() . The methods are given below. Let’s take an example by using one of the methods mentioned above to know how to use the methods with parameters. Import the required libraries using the below code. import numpy as np
import matplotlib.pyplot as plt
from scipy import stats
Create observation data values and calculate the log probability from these data values with mean = 0 and standard deviation = 1 . observatin_x = np.linspace(-2,2,200)
logpdf_norm = stats.norm.logpdf(observatin_x,loc=0,scale=1)
Plot the created distribution using the below code. plt.plot(observatin_x,logpdf_norm)
plt.xlabel('x-values')
plt.ylabel('logpdf_norm_values')
plt.title("Log probability of normal distribution")
plt.show() Python Scipy Stats Norm LogpdfThis is how to compute
the log pdf of norm using the method norm.logpdf() of Python Scipy. Read: Python Scipy Special Module Python Scipy Stats Norm LogcdfThe object norm() has a method logcdf() that calculates the log cumulative distribution of norm. The syntax is given below. scipy.stats.norm.logcdf(x,loc,size,scale)
Where parameters are: - x: It is a set of points or values that represent evenly sampled data in the form of array data.
- loc: It is used to specify the mean, by default it is 0.
- scale: It is used to determine the standard deviation, by default it is 1.
The above parameters are the standard parameter of all the methods in the object scipy.stats.norm() . The methods are given below. Import the required libraries using the below code. import numpy as np
import matplotlib.pyplot as plt
from scipy import stats
Create observation data values and calculate the log cumulative from these data values with mean = 0 and standard deviation = 1 . observatin_x = np.linspace(-5,5,200)
logcdf_norm = stats.norm.logcdf(observatin_x,loc=0,scale=1)
Plot the created distribution using the below code. plt.plot(observatin_x,logcdf_norm)
plt.xlabel('x-values')
plt.ylabel('logcdf_norm_values')
plt.title("Log cumulative distribution of normal distribution")
plt.show() Python Scipy Stats Norm LogcdfThis is how to compute the log cdf of the norm using the method norm.logcdf() of Python Scipy. Read: Scipy Linalg – Helpful Guide Python Scipy Stats Norm GenThe scipy.stats.genpareto represents the generalized Pareto random variable that is continuous. It has different kinds of functions of normal distribution like CDF, PDF, median, etc. The generalized
Pareto distribution (GPD) is a class of continuous probability distributions used in statistics. It is frequently used to model another distribution’s tails. It has two important parameters loc for the mean and scale for standard deviation, as we know we control the shape and location of distribution using these parameters. The syntax is given below. scipy.stats.genpareto.method_name(x,c,loc,size,moments,scale)
Where parameters are: - x: It is a set of points or values that represent evenly sampled
data in the form of array data.
- c: It is used to specify the shape.
- loc: It is used to specify the mean, by default it is 0.
- moments: It is used to calculate statistics like standard deviation, kurtosis, and mean.
- scale: It is used to specify the standard deviation, by default it is 1.
The above parameters are the common parameter of all the methods in the object scipy.stats.genpareto() . The methods
are given below. - scipy.stats.genpareto.cdf(): It is used for the cumulative distribution function.
- scipy.stats.genpareto.pdf(): It is used for the probability density function.
- scipy.stats.genpareto.rvs(): To get the random variates.
- scipy.stats.genpareto.stats(): It is used to get the standard deviation, mean, kurtosis, and skew.
- scipy.stats.genpareto.logpdf():
It is used to get the log related to the probability density function.
- scipy.stats.genpareto.logcdf(): It is used to find the log related to the cumulative distribution function.
- scipy.stats.genpareto.sf(): It is used to get the values of the survival function.
- scipy.stats.genpareto.isf(): It is used to get the values of the inverse survival function.
- scipy.stats.genpareto.logsf():
It is used to find the log related to the survival function.
- scipy.stats.genpareto.mean(): It is used to find the mean related to the normal distribution.
- scipy.stats.genpareto.medain(): It is used to find the median related to the normal distribution.
- scipy.stats.genpareto.var(): It is used to find the variance related to the distribution.
- scipy.stats.genpareto.std():
It is used to find the standard deviation related to the distribution
Let’s take an example by using one of the methods mentioned above to know how to use the methods with parameters. Import the required libraries using the below code. from scipy.stats import genpareto
import matplotlib.pyplot as plt
import numpy as np
Code creates a variable for the shape parameters and assigns some values. c = 0.2
Create an array of data using the method ppf() of an object genpareto using the below code. array_data = np.linspace(genpareto.ppf(0.01, c),
genpareto.ppf(0.90, c), 90)
array_data Python Scipy Stats Norm Genpareto
Example
Now plot the probability density function by accessing the method pdf() of an object genpareto of the module scipy.stats using the below code. fig, ax = plt.subplots(1, 1)
ax.plot(array_data, genpareto.pdf(array_data, c),
'r-', lw=4, alpha=0.5, label='genpareto PDF') Scipy Stats GenparetoThis is how to use genpareto() of Python Scipy to model the distribution tails. Read: Scipy Normal Distribution Python Scipy Stats Norm GennormThe scipy.stats.gennorm represents the random variable that is generalized normal continuous. It has different kinds of functions of
normal distribution like CDF, PDF, median, etc. It has two important parameters loc for the mean and scale for standard deviation, as we know we control the shape and location of distribution using these parameters. The syntax is given below. scipy.stats.gennorm.method_name(x,beta,loc,size,moments,scale)
Where parameters are: - x: It is a set of points or values that represent evenly sampled data in the form of array data.
- beta: It is used to specify the shape.
- loc:
It is used to specify the mean, by default it is 0.
- moments: It is used to calculate statistics like standard deviation, kurtosis, and mean.
- scale: It is used to specify the standard deviation, by default it is 1.
The above parameters are the common parameter of all the methods in the object scipy.stats.gennorm() . The methods are given below. - scipy.stats.gennorm.CDF(): It is used for the cumulative distribution
function.
- scipy.stats.gennorm.PDF(): It is used for the probability density function.
- scipy.stats.gennorm.rvs(): To get the random variates.
- scipy.stats.gennorm.stats(): It is used to get the standard deviation, mean, kurtosis, and skew.
- scipy.stats.gennorm.logPDF(): It is used to get the log related to the probability density
function.
- scipy.stats.gennorm.logCDF(): It is used to find the log related to the cumulative distribution function.
- scipy.stats.gennorm.sf(): It is used to get the values of the survival function.
- scipy.stats.gennorm.isf(): It is used to get the values of the inverse survival function.
- scipy.stats.gennorm.logsf(): It is used to
find the log related to the survival function.
- scipy.stats.gennorm.mean(): It is used to find the mean related to the normal distribution.
- scipy.stats.gennorm.medain(): It is used to find the median related to the normal distribution.
- scipy.stats.gennorm.var(): It is used to find the variance related to the distribution.
- scipy.stats.gennorm.std():
It is used to find the standard deviation related to the distribution
Let’s take an example by using one of the methods mentioned above to know how to use the methods with parameters. Import the required libraries using the below code. from scipy.stats import gennorm
import matplotlib.pyplot as plt
import numpy as np
Code creates a variable for the shape parameters and assigns some values. beta = 1.4
Create an array of data using the method ppf() of an object gennorm using the below code. array_data = np.linspace(gennorm.ppf(0.01, a),
gennorm.ppf(0.90, a,b), 90)
array_data Python Scipy Stats Norm GennormNow plot
the probability density function by accessing the method PDF() of an object gennorm of the module scipy.stats using the below code. fig, ax = plt.subplots(1, 1)
ax.plot(array_data, gennorm.pdf(array_data, beta),
'r-', lw=4, alpha=0.5, label='gennorm PDF') Python Scipy Stats Norm Gennorm ExampleThis is how to use the method norm.gennorm() of Python Scipy. Read: Scipy Convolve – Complete Guide Python Scipy Stats Norm RvsThe method rvs() of Python Scipy of object norm is random variates that generate random numbers. The syntax is
given below scipy.stats.norm.rvs(loc=0, scale=1, size=1, random_state=None)
Where parameters are: - loc: It is a mean.
- scale: The distribution’s matrix of covariance.
- size(int): It is the sample size.
- random_state(int): If the seed is None, the NumPy.random method is utilized (or np.random). It uses a single instance of RandomState. If the seed is an integer, a new RandomState object is made using the seed. If the seed already has a Generator or
RandomState instance, that instance is used.
Let’s draw a random sample from a multivariate normal distribution by following the below steps: Import the required libraries using the below python code. from scipy import stats
Create a multivariate normal distribution using the below code. norm_dist = stats.norm()
Generate random numbers using normal distribution using the below code. samp_size = 100000
norm_dist.rvs(samp_size) Python Scipy Stats Norm RvsThis is how to generate the random numbers using the method norm.rvs() of python
Scipy. Read: Scipy Integrate + Examples Python Scipy Stats Norm FitThe method fit() of Python Scipy of object norm that provides approximations for scale and location. The syntax is given below. scipy.stats.norm.fit(data)
Where parameter data is the data for which we need the location and scale. Let’s understand with an example by following steps: Import the required libraries or methods using the below code. from scipy.stats import norm
Generate random numbers using the method norm.rvs() . x_data = norm.rvs(1., 2., size=500, random_state=123)
Now fit the above data using the below code. loc_, scale_ = norm.fit(x_data)
Check the estimated parameter values using the below code. print("loc is ",loc_)
print("Scale is ",scale_) Python Scipy Stats Norm FitAlso, take a look at some more Python SciPy tutorials. - Scipy Sparse – Helpful Tutorial
- Scipy Optimize – Helpful Guide
- Scipy Ndimage Rotate
- Scipy Misc + Examples
So, in this tutorial, we have learned about the “Python
Scipy Stats Norm” and covered the following topics. - What is Norm in Statistics
- Python Scipy Stats Norm Pdf
- Python Scipy Stats Norm Expect
- Python Scipy Stats Norm Plot
- Python Scipy Stats Norm Parameters
- Python Scipy Stats Norm Cdf
- Python Scipy Stats Norm Interval
- Python Scipy Stats Norm Ppf
- Python Scipy Stats Norm Gen
- Python Scipy Stats Norm Logpdf
- Python Scipy Stats Norm Logcdf
- Python
Scipy Stats Norm Gennorm
- Python Scipy Stats Norm Rvs
- Python Scipy Stats Norm Fit
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