## Simulate and Compare TQQQ and QQQ

This tutorial utilizes Python to simulate and compare the performance of TQQQ and QQQ. The fundamental observation is that TQQQ tends to outperform QQQ when the number of up days exceeds the number of down days. Conversely, if the market experiences an equal number of up days and down days, TQQQ is expected to underperform … Read more

## What is a Statistic

This tutorial provides definitions and examples of a statistic. Further, it explains the relationship between a statistic and sampling distribution. The Definition of a Statistic A statistic is a function of observable random variables, T=t(X1, X2, …, Xn), which does not depend on any unknown parameters. script t is the function that we apply to … Read more

## Comparisons of t-distribution and Normal distribution

This tutorial compares t-distribution and normal distribution by explaining the similarities and connections between t-distribution and normal distribution. Similarities between t-distribution and normal distribution There are a few similarities between t-distribution and normal distribution. The following figure shows the t-distribution density function curve and the standard normal curve. As we can see, as the sample … Read more

## Major Python Packages for Hypothesis Testing

The 2 popular Python packages for hypothesis testing are scipy.stats and statsmodels. The following includes a brief introduction to each of them, along with simple examples. Introduction of Scipy.stats Based on scipy.stats official webpage, the module contains a large number of probability distributions, summary and frequency statistics, correlation functions and statistical tests, and more. Example … Read more

## What Is Hypothesis Testing

Definition of Hypothesis Testing Hypothesis Testing is an inferential statistical method using sample data to solve assumptions about population parameters. For instance, you want to test if people in New York City’s attitudes toward the new iPhone (e.g., iPhone 14) on a 7-point scale (1 = not at all, 7 = like it a lot) is … Read more

## How to change column names of Pandas DataFrames

There are 2 methods of changing the column names of Pandas Dataframes. The following shows the basic Python code syntax for changing column names of Pandas Dataframes. Method 1: df.rename(columns={‘old_name_1′:’new_name_1’, ‘old_name_2′:’new_name_2’}, inplace=True) Method 2: df = df.rename({‘old_name_1′:’new_name_1’, ‘old_name_2′:’new_name_2’}, axis=1) Example 1 of changing column names of Pandas DataFrames (Method 1) The following is the first … Read more

## Combine Lists into an Array in Python

You can use Numpy column_stack() or row_stack() to combine lists into an array. As Columns: np.column_stack((list1, list2,…)) As Rows: np.row_stack((list1, list2,…)) Example 1 of lists to columns The following combines lists into an array using column_stack(). Thus, lists become columns in the array. [[6 2 4] [2 1 1] [3 3 2] [4 4 4] … Read more

## Check if an item in a Python list

This tutorial shows examples of checking if an item is in a Python list. Method 1: item in list_name Method 2: list_name.index(item) Method 3: list_name.count(item) Example for method 1: Check if an item in a list The following code checks if the item of number 6 is in a list. The following is the output, … Read more

## Count the Number of NaN in Pandas Dataframes

This tutorial uses 2 examples to show how to count the number of NaN in Pandas dataframes. Method 1: count the number of NaN by columns: df.isnull().sum() Method 2: count the number of NaN in the whole dataframe: df.isnull().sum().sum() Example for Method 1 The following counts the number of NaN by columns using df.isnull().sum(). The … Read more

## How to Subset Rows in Pandas Dataframes

There are at least 4 methods to subset row in Pandas dataframes. Method 1: loc[[Comma]] df.loc[[row_number1, row_number_2]] Method 2: loc[Colon] df.loc[row_number1: row_number_2] Method 3: iloc[[Comma]] df.iloc[[row_number1, row_number_2]] Method 4: iloc[Colon] df.iloc[[row_number1: row_number_2]] Example 1 for Method 1 The following uses loc[[Comma]] (i.e., loc[[0,2]])to subset rows in a Pandas dataframe. The following shows the original dataframe … Read more