# Smirnov s system for making money on the Internet, Find Hotels in Smirnov's Residence, Moscow

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Photo by Nerfee Mirandilla on Unsplash Motivation Hypothesis testing is used in many applications and the methodology seems quite straightforward. Often times, though, we tend to overlook the underlying assumptions and need to ask: Are we comparing apples to oranges?

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The question also arises when data scientists decide to discard observations based on missing features. Imagine we have features f1, f2,… fn and a binary target variable y. Assuming many observations have missing information for one or more features, we decide to drop these observations rows.

By doing so we might have altered the distribution of a feature fk.

To formulate this as a question: Does Smirnov s system for making money on the Internet observations change the distribution of feature s?

Is this change significant?

In this article, we are going to present some assumptions of the t-test and how the Kolmogorov—Smirnov KS test can validate or discredit those assumptions. That being said, it is crucial to state early on that the t-test and KS test are testing different things. For each step we will present the theory and implement the code in Python 3.

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The t-test assumes that situations produce normal data that differ only in the sense that the average outcome in one situation is different from the average outcome of the other situation. That being said, if we apply the t-test to data drawn from a non-normal distribution, we are probably increasing the risk of errors.

Small Datasets With the Same Mean Consider the two randomly generated samples in the code block below: Both samples are generated from normal distributions having the same mean, however by visual inspection it is clear that both samples are different.

A t-test might not be able to pick up on this difference and confidently say that both samples are identical. A t-test with scipy.

We therefore cannot reject the null hypothesis of identical average scores.

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Different Mean and Same Distribution Say we generate two options with a deposit of 1 datasets that differ in mean, but a non-normal distribution masks the difference as shown in the code below: If we knew in advance that the data was not normally distributed we would not be using the t-test to begin with. With this idea in mind, we introduce a method to check if our observations come from a reference probability distribution.

Also, the credit risk evaluation is usually made by using the application card scoring model, which has the shortcomings of strict data assumption and inability to process complex data. In order to overcome the limitations of the credit card scoring model and evaluate credit risk better, this paper proposes a credit evaluation model based on extreme gradient boosting tree XGBoost machine learning ML algorithm to construct a credit risk assessment model for Internet financial institutions. At the same time, an Internet lending company in China is taken as a case study to compare the performance of the traditional credit card scoring model and the proposed machine learning ML algorithm model. The results show that ML algorithm has a very significant advantage in the field of Internet financial risk control, it has more accurate prediction results and has no particularly strict assumptions and restrictions on data, and the process of processing data is more convenient and reliable. We should increase the application of ML in the field of financial risk control.

The KS test can be used to compare a sample with a reference probability distribution, or to compare two samples. Suppose we have observations x1, x2, …xn that we think come from a distribution P.

### Theory, Application, and Interpretation

Distributions such as the normal distribution are known to have a mean of 0 and a standard deviation of 1. More specifically, we will use the Empirical Distribution Function EDF : an estimate of the cumulative distribution function that generated the points in the sample.

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The usefulness of the CDF is that it uniquely characterizes a probability distribution. Test if Sample Belongs to Distribution In the first example let the null hypothesis be that our samples come from a normal distribution N 0,1.

We want to compare the empirical distribution function of the observed data, with the cumulative distribution function associated with the null hypothesis.