The Central Limit Theorem with Python

Statistics is a fundamental discipline for the analysis and interpretation of data. One of the most powerful conceptual tools in statistics is the Central Limit Theorem (CLT). This theorem is crucial to inferential statistics and provides the basis for many statistical analyzes applied in a wide range of fields.

In this article, we will explore together the differences between descriptive statistics and inferential statistics, highlighting their specific roles in statistical analysis and illustrating how they can be used in a complementary way to obtain a complete understanding of the data.

The Probability Density Function (PDF) is a mathematical function that describes the relative probability of a random variable taking on certain values. In other words, it provides a representation of the probability distribution of a continuous variable. The PDF is non-negative and the area under the curve is 1, as it represents the total probability. For example, in the normal distribution, the PDF is represented by a bell curve.

The Student’s t-distribution is a probability distribution that derives from the concept of t-statistics. It is often used in statistical inference when the sample on which an analysis is based is relatively small and the population standard deviation is unknown. The shape of the t distribution is similar to the normal one, but has thicker tails, making it more suitable for small sample sizes.

Kurtosis is a statistical measure that describes the shape of the distribution of a data set. Essentially, it indicates how much the tails of a distribution differ from those of a normal distribution. A kurtosis value greater than zero suggests heavier tails (more “pointed” distribution), while a lower value indicates lighter tails (more “flat” distribution). Kurtosis can be positive (the tails are heavier), negative (the tails are lighter), or zero (similar to a normal distribution).

Skewness is a statistical measure that describes the skewness of the distribution of a data set. Indicates whether the tail of the distribution is shifted to the left or to the right compared to its central part. Positive skewness indicates a longer tail on the right, while negative skewness indicates a longer tail on the left.