Python data visualization normal distribution simple analysis and implementation code, python Visualization

Python data visualization normal distribution simple analysis and implementation code, python Visualization

Python is simple but not simple, especially when combined with high numbers...

Normaldistribution, also known as "Normal Distribution", also known as Gaussiandistribution, was first obtained by A. momowt in the formula for finding the two-term distribution. C. F. Gauss derives the measurement error from another angle. P.S. Laplace and Gauss study its properties. It is a probability distribution that is very important in mathematics, physics and engineering, and has a significant influence in many aspects of statistics.

The normal curve is bell-shaped, the two sides are low, the middle is high, and the left and right symmetry is called a bell-shaped curve because the curve is bell-shaped.

If the random variable X follows a normal distribution where the expected mathematical value is μ and the variance is σ ^ 2, it is recorded

N (μ, σ ^ 2)

The probability density function determines its location based on the expected value μ of the normal distribution, and its standard deviation σ determines the distribution range. When μ = 0, σ = 1, the normal distribution is the standard normal distribution. Its probability density function is:

The standard normal distribution we usually call a normal distribution:

Probability Density Function

Code implementation:

# Python implementation of normal distribution
 # Draw normal distribution probability density function
 u = 0 # mean μ
 u01 = -2
 sig = math.sqrt (0.2) # standard deviation δ
 sig01 = math.sqrt (1)
 sig02 = math.sqrt (5)
 sig_u01 = math.sqrt (0.5)
 x = np.linspace (u-3 * sig, u + 3 * sig, 50)
 x_01 = np.linspace (u-6 * sig, u + 6 * sig, 50)
 x_02 = np.linspace (u-10 * sig, u + 10 * sig, 50)
 x_u01 = np.linspace (u-10 * sig, u + 1 * sig, 50)
 y_sig = np.exp (-(x-u) ** 2 / (2 * sig ** 2)) / (math.sqrt (2 * math.pi) * sig)
 y_sig01 = np.exp (-(x_01-u) ** 2 / (2 * sig01 ** 2)) / (math.sqrt (2 * math.pi) * sig01)
 y_sig02 = np.exp (-(x_02-u) ** 2 / (2 * sig02 ** 2)) / (math.sqrt (2 * math.pi) * sig02)
 y_sig_u01 = np.exp (-(x_u01-u01) ** 2 / (2 * sig_u01 ** 2)) / (math.sqrt (2 * math.pi) * sig_u01)
 plt.plot (x, y_sig, "r-", linewidth = 2)
 plt.plot (x_01, y_sig01, "g-", linewidth = 2)
 plt.plot (x_02, y_sig02, "b-", linewidth = 2)
 plt.plot (x_u01, y_sig_u01, "m-", linewidth = 2)
 # plt.plot (x, y, 'r-', x, y, 'go', linewidth = 2, markersize = 8)
 plt.grid (True)
 plt.show () 

Summary

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