Understanding PDF Definition in Stat Theory | Question on Divisor & Histogram

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In summary, a pdf (probability density function) is defined as the limit of the ratio of a histogram function, H, and the width, Δc, as the observation number, N, and the width approach infinity and zero, respectively. This division is necessary to ensure that the integral of the pdf remains 1.
  • #1
member 428835
hey pf!

can someone help me understand why a pdf is defined in the following manner: [tex]\lim_{\substack{N\to \infty\\ \Delta c \to 0}}\frac{H(c,\Delta c,N)}{\Delta c}[/tex] where [itex]\Delta c[/itex] is the width, [itex]N[/itex] is the observation number? Specifically, why the divisor? why is this necessary? [itex]H[/itex] is a histogram.

any insight is greatly appreciated!

thanks!
 
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  • #2
I'm not familiar with your notation. However, in general, the integral of a pdf must be 1, so I presume the division is to insure that this holds.
 
  • #3
sorry, i was worried about being too vague, but i think youre right.
 

FAQ: Understanding PDF Definition in Stat Theory | Question on Divisor & Histogram

What is a PDF in statistical theory?

A PDF (Probability Density Function) is a mathematical function that describes the probability of a continuous random variable taking on a certain value or falling within a certain range of values. It is used to understand the distribution of data and is a fundamental concept in statistical theory.

How is a PDF different from a CDF?

A PDF represents the probability of a random variable taking on a specific value, while a CDF (Cumulative Distribution Function) represents the probability of a random variable being less than or equal to a specific value. In other words, a PDF shows the probability of a single outcome, while a CDF shows the probability of a range of outcomes.

What is the purpose of a divisor in a PDF?

In a PDF, the divisor is used to normalize the function so that the area under the curve is equal to 1. This allows the PDF to represent probabilities as percentages, making it easier to interpret and compare different PDFs.

How can a histogram be used to understand a PDF?

A histogram is a graphical representation of a PDF that shows the frequency of data falling within different intervals or bins. By visually displaying the distribution of data, a histogram can help in understanding the shape of a PDF and identifying any patterns or outliers in the data.

How does understanding PDFs help in statistical analysis?

PDFs are essential in statistical analysis as they provide a way to mathematically describe and analyze the distribution of data. They allow for the calculation of probabilities and can be used to make predictions and draw conclusions about a population based on a sample of data. PDFs are also used in many statistical tests and models to make inferences and draw conclusions from data.

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