Distribution Properties: Skewness, Kurtosis, and Tails
Advanced distribution properties like skewness and kurtosis help you uncover deeper patterns in retail data that basic summary statistics cannot reveal.
Why These Measures Matter in Retail
- Identify asymmetries: detect if your sales, revenue, or customer behavior data is lopsided or has unexpected trends;
- Spot unusual patterns: find outliers or extreme values that could affect inventory or risk management;
- Improve business decisions: use insights from these properties to guide promotions, stock planning, and performance forecasting.
Key Concepts
- Skewness: measures how much a distribution leans to one side, showing if most values are above or below the average;
- Kurtosis: describes how heavy or light the tails of a distribution are, revealing the likelihood of extreme values.
Understanding skewness and kurtosis lets you judge how typical or unusual your retail data is, so you can make smarter, data-driven decisions.
1234567891011121314151617181920import pandas as pd from scipy.stats import skew, kurtosis # Sample retail dataset data = { "daily_sales": [200, 220, 210, 250, 300, 800, 210, 205, 220, 215], "transaction_amount": [20, 22, 21, 25, 30, 80, 21, 20.5, 22, 21.5] } df = pd.DataFrame(data) # Compute skewness and kurtosis for key numerical features sales_skew = skew(df["daily_sales"]) sales_kurt = kurtosis(df["daily_sales"]) amount_skew = skew(df["transaction_amount"]) amount_kurt = kurtosis(df["transaction_amount"]) print(f"Skewness of daily_sales: {sales_skew:.2f}") print(f"Kurtosis of daily_sales: {sales_kurt:.2f}") print(f"Skewness of transaction_amount: {amount_skew:.2f}") print(f"Kurtosis of transaction_amount: {amount_kurt:.2f}")
Interpreting skewness and kurtosis helps you understand the shape and risks in your retail data:
- Positive skewness in
daily_sales:- Most days have moderate sales;
- A few days have exceptionally high sales (often due to promotions or holidays);
- The right tail of the distribution is longer or fatter.
- Negative skewness:
- More frequent low sales days with occasional sharp drops;
- The left tail of the distribution is longer.
- Kurtosis:
- Measures the likelihood of extreme sales values;
- High kurtosis means more outliers or "heavy tails"—increasing the risk of unexpected spikes or drops.
Understanding these properties lets you:
- Anticipate unusual demand;
- Manage stock more effectively;
- Set realistic expectations for sales performance.
12345678910import matplotlib.pyplot as plt import seaborn as sns # Visualize the distribution of a skewed retail feature plt.figure(figsize=(8, 4)) sns.histplot(df["daily_sales"], kde=True, color="skyblue", bins=8) plt.title("Distribution of Daily Sales") plt.xlabel("Daily Sales") plt.ylabel("Frequency") plt.show()
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Advanced distribution properties like skewness and kurtosis help you uncover deeper patterns in retail data that basic summary statistics cannot reveal.
Why These Measures Matter in Retail
- Identify asymmetries: detect if your sales, revenue, or customer behavior data is lopsided or has unexpected trends;
- Spot unusual patterns: find outliers or extreme values that could affect inventory or risk management;
- Improve business decisions: use insights from these properties to guide promotions, stock planning, and performance forecasting.
Key Concepts
- Skewness: measures how much a distribution leans to one side, showing if most values are above or below the average;
- Kurtosis: describes how heavy or light the tails of a distribution are, revealing the likelihood of extreme values.
Understanding skewness and kurtosis lets you judge how typical or unusual your retail data is, so you can make smarter, data-driven decisions.
1234567891011121314151617181920import pandas as pd from scipy.stats import skew, kurtosis # Sample retail dataset data = { "daily_sales": [200, 220, 210, 250, 300, 800, 210, 205, 220, 215], "transaction_amount": [20, 22, 21, 25, 30, 80, 21, 20.5, 22, 21.5] } df = pd.DataFrame(data) # Compute skewness and kurtosis for key numerical features sales_skew = skew(df["daily_sales"]) sales_kurt = kurtosis(df["daily_sales"]) amount_skew = skew(df["transaction_amount"]) amount_kurt = kurtosis(df["transaction_amount"]) print(f"Skewness of daily_sales: {sales_skew:.2f}") print(f"Kurtosis of daily_sales: {sales_kurt:.2f}") print(f"Skewness of transaction_amount: {amount_skew:.2f}") print(f"Kurtosis of transaction_amount: {amount_kurt:.2f}")
Interpreting skewness and kurtosis helps you understand the shape and risks in your retail data:
- Positive skewness in
daily_sales:- Most days have moderate sales;
- A few days have exceptionally high sales (often due to promotions or holidays);
- The right tail of the distribution is longer or fatter.
- Negative skewness:
- More frequent low sales days with occasional sharp drops;
- The left tail of the distribution is longer.
- Kurtosis:
- Measures the likelihood of extreme sales values;
- High kurtosis means more outliers or "heavy tails"—increasing the risk of unexpected spikes or drops.
Understanding these properties lets you:
- Anticipate unusual demand;
- Manage stock more effectively;
- Set realistic expectations for sales performance.
12345678910import matplotlib.pyplot as plt import seaborn as sns # Visualize the distribution of a skewed retail feature plt.figure(figsize=(8, 4)) sns.histplot(df["daily_sales"], kde=True, color="skyblue", bins=8) plt.title("Distribution of Daily Sales") plt.xlabel("Daily Sales") plt.ylabel("Frequency") plt.show()
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