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Chapter 4 Continuous distributions

Consider a real life inspired situation with a company called “Pep Zone”, selling auto parts and supplies, including motor oil. They implemented a simple inventory management system: when their stock of oil drops below 80 litres, they place an order for replenishment. They got in touch with us because they are not sure whether their approach is sensible and they feel that they might be loosing sales because of it.

While this case might sound very distant from statistics, it can be solved directly using the topics discussed in this chapter. This is because the number of litres is a continuous variable, the demand on which can be fractional. If we were to work for a company, we would probably need to look at the distribution of demand on the motor oil and then based on that we could come up with some recommendations.

So, in this chapter we will discuss what is continuous distribution and consider several vital distributions, which are often used in practice:

1. Uniform in Section 4.2;
2. Normal in Section 4.3;
3. Log-Normal, which is directly connected to (2) in Section 4.4;
4. Exponential, in Section 4.5.

While there exist many more distributions, we cannot discuss all of them and focus only on the most important ones.

Another important topic that we will discuss in this chapter is the convolution of distributions (when several random variables are added up). Understanding the idea behind this is essential in understanding the material from Chapter 6.