Continuous distributions

Introduction to Statistics in Python

Maggie Matsui

Content Developer, DataCamp

Waiting for the bus

Continuous uniform distribution

Continuous uniform distribution

Probability still = area

$$P(4 \le \text{wait time} \le 7) = ~~ ?$$

Probability still = area

$$P(4 \le \text{wait time} \le 7) = ~~ ?$$

Probability still = area

$$P(4 \le \text{wait time} \le 7) = 3 \times 1/12 = 3/12$$

Uniform distribution in Python

$$ P(\text{wait time} \le 7)$$

from scipy.stats import uniform

uniform.cdf(7, 0, 12)

0.5833333

"Greater than" probabilities

$$ P(\text{wait time} \ge 7) = 1 - P(\text{wait time} \le 7)$$

from scipy.stats import uniform
1 - uniform.cdf(7, 0, 12)

0.4166667

$$ P(4 \le \text{wait time} \le 7)$$

$$ P(4 \le \text{wait time} \le 7)$$

$$ P(4 \le \text{wait time} \le 7)$$

from scipy.stats import uniform
uniform.cdf(7, 0, 12) - uniform.cdf(4, 0, 12)

0.25

Total area = 1

$$P(0 \le \text{wait time} \le 12) = ~~ ?$$

Total area = 1

$$P(0 \le \text{outcome} \le 12) = 12 \times 1/12 = 1$$

Generating random numbers according to uniform distribution

from scipy.stats import uniform
uniform.rvs(0, 5, size=10)

array([1.89740094, 4.70673196, 0.33224683, 1.0137103 , 2.31641255,
       3.49969897, 0.29688598, 0.92057234, 4.71086658, 1.56815855])

Other continuous distributions

 

 

Other continuous distributions

 

 

Other special types of distributions

Normal distribution

Exponential distribution

Let's practice!

Introduction to Statistics in Python