Why is normalization of a probability distribution important

To start off, let's imagine that you need to compare temperatues from cities around the world. If you measure NYC, the data will most likely be in fahrenheit. And in Poland, the temperatues will be listed in celsius. At its most basic, the normalization process will take the data from each city and convert the temperatues to use the same unit of measure.

I think that's a little more straightforward than the Wikipedia example. But that's simply the base case. Now let's discuss an important task in machine learning, feature scaling. This conversion process is called standardizing or normalizing.

It requires knowing the population parameters, not the statistics of a sample drawn from the population of interest. However, knowing the true standard deviation of a population is often unrealistic except in cases such as standardized testing, where the entire population is measured.

In cases where it is impossible to measure every member of a population, a random sample may be used. Normal Distribution and Scales : Compares the various grading methods in a normal distribution.

Privacy Policy. Skip to main content. Continuous Random Variables. Search for:. Normal Approximation. The Normal Approximation to the Binomial Distribution The process of using the normal curve to estimate the shape of the binomial distribution is known as normal approximation.

Learning Objectives Explain the origins of central limit theorem for binomial distributions. Key Takeaways Key Points Originally, to solve a problem such as the chance of obtaining 60 heads in coin flips, one had to compute the probability of 60 heads, then the probability of 61 heads, 62 heads, etc, and add up all these probabilities.

Abraham de Moivre noted that when the number of events coin flips increased, the shape of the binomial distribution approached a very smooth curve.

Key Terms normal approximation : The process of using the normal curve to estimate the shape of the distribution of a data set. The Scope of the Normal Approximation The scope of the normal approximation is dependent upon our sample size, becoming more accurate as the sample size grows. Learning Objectives Explain how central limit theorem is applied in normal approximation.

The scope of the normal approximation follows with the statistical themes of the law of large numbers and central limit theorem. According to the law of large numbers, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.

Key Terms central limit theorem : The theorem that states: If the sum of independent identically distributed random variables has a finite variance, then it will be approximately normally distributed. Calculating a Normal Approximation In this atom, we provide an example on how to compute a normal approximation for a binomial distribution. Learning Objectives Demonstrate how to compute normal approximation for a binomial distribution. Key Takeaways Key Points In our example, we have a fair coin and wish to know the probability that you would get 8 heads out of 10 flips.

A total of 8 heads is 1. Because the binomial distribution is discrete an the normal distribution is continuous, we round off and consider any value from 7. Using this approach, we calculate the area under a normal curve which will be the binomial probability from 7.

Change of Scale In order to consider a normal distribution or normal approximation, a standard scale or standard units is necessary. Learning Objectives Explain the significance of normalization of ratings and calculate this normalization. Key Takeaways Key Points In the simplest cases, normalization of ratings means adjusting values measured on different scales to a notionally common scale, often prior to averaging.

The standard score is a dimensionless quantity obtained by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation. Key Terms datum : A measurement of something on a scale understood by both the recorder a person or device and the reader another person or device. It is important not to get this confused with asking whether a distribution is normal , i. Sign up to join this community. The best answers are voted up and rise to the top.

Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. What does "normalization" mean and how to verify that a sample or a distribution is normalized? Ask Question. Asked 8 years, 1 month ago. Active 3 years, 8 months ago. Viewed 80k times. For one, what does it mean for any distribution to be normalized?

And two, how do we go about verifying whether a distribution is normalized or not? Improve this question. Ada Ada 1 1 gold badge 5 5 silver badges 6 6 bronze badges.

For example, in the case of the uniform, some people may mean "linearly rescaled so as to get a standard uniform" i. For the uniform, I'd normally assume the first, but as you see from an answer below, other people may take it to mean something else.