What do you believe is the single most important factor driving up the cost of living in Nigeria?

As is well known, the normal distribution is a key tool in probability and statistics. It can be described as a distribution that obeys a universal rule derived from one of the most important theorems in probability: the central limit theorem, often called the CLT. More practically, it also describes how some data naturally cluster around a central value, the shape of whose corresponding histograms (representing the distribution of the data) is a well equilibrated bell curve.

Some data from real-world processes follow this pattern, making the normal distribution an option for their analysis. However, the ideal bell shape is highly unexpected for most data. In fact, sometimes the data is skewed, meaning that the associated histograms are tilted to one side, left or right. In other cases, the data may have several modes (peaks) rather than a central value. These variations make the normal distribution less accurate for analyzing such data sets.

Mathematical theory helps to deal with these problems. By introducing adjustments for skewness and kurtosis, we can modify the shape possibilities of the normal distribution. On the other hand, transformation techniques can handle multiple modes, providing a more flexible approach. In essence, mathematical theory provides the necessary tools to extend the normal distribution to make it more useful for different types of data. This improves the accuracy of models and predictions, and therefore decision making.

Several strategies already exist, but rare are those that can simultaneously skew and add modes to the normal distribution through a highly tunable configuration. Such an option is developed in the paper "A new mathematical solution for creating asymmetric continuous distributions," published in the journal Asymmetry.

Using two almost unconstrained parameters and a very general intermediate function, the theoretical foundations and guarantees of a new mathematical strategy are laid. The key to this strategy lies in the infinite possibilities for the choice of these components; the intermediate function can be chosen as exponential, logarithmic, trigonometric, among a wide range of functional types. Depending on their nature, various right-skewed, left-skewed and multimodal shapes can be reached.

• Read More