density

(noun)

the probability that an event will occur, as a function of some observed variable

Related Terms

Examples of density in the following topics:

  • The Density Scale

    • Density estimation is the construction of an estimate based on observed data of an unobservable, underlying probability density function.
    • Histograms are used to plot the density of data, and are often a useful tool for density estimation.
    • Density estimation is the construction of an estimate based on observed data of an unobservable, underlying probability density function.
    • The unobservable density function is thought of as the density according to which a large population is distributed.
    • A probability density function, or density of a continuous random variable, is a function that describes the relative likelihood for this random variable to take on a given value.

  • Continuous Probability Distributions

    • A continuous probability distribution is a probability distribution that has a probability density function.
    • The probability density function is nonnegative everywhere, and its integral over the entire space is equal to one.
    • Unlike a probability, a probability density function can take on values greater than one.
    • The standard normal distribution has probability density function:
    • Boxplot and probability density function of a normal distribution $$$N(0, 2)$.

  • From histograms to continuous distributions

    • This smooth curve represents a probability density function (also called a density or distribution), and such a curve is shown in Figure 2.28 overlaid on a histogram of the sample.
    • A density has a special property: the total area under the density's curve is 1.
    • Density for heights in the US adult population with the area between 180 and 185 cm shaded.

  • Continuous Sampling Distributions

    • Therefore, these values are called probability densities rather than probabilities.
    • A probability density function, or density of a continuous random variable, is a function that describes the relative likelihood for this random variable to take on a given value.
    • The probability for the random variable to fall within a particular region is given by the integral of this variable's density over the region .
    • Boxplot and probability density function of a normal distribution $N(0, 2)$.

  • Multiple Regression Models

    • You've gone to a number of beaches that already have the beetles and measured the density of tiger beetles (the dependent variable) and several biotic and abiotic factors, such as wave exposure, sand particle size, beach steepness, density of amphipods and other prey organisms, etc.
    • Multiple regression would give you an equation that would relate the tiger beetle density to a function of all the other variables.
    • For example, if you did a regression of tiger beetle density on sand particle size by itself, you would probably see a significant relationship.
    • If you did a regression of tiger beetle density on wave exposure by itself, you would probably see a significant relationship.
    • Maybe sand particle size is really important, and the correlation between it and wave exposure is the only reason for a significant regression between wave exposure and beetle density.

  • Summary of the Uniform and Exponential Probability

    • Probability density function: f (X) = $\frac{1}{ ba }$ for a≤ X ≤b

  • Properties of Continuous Probability Distributions

    • The curve is called the probability density function (abbreviated: pdf).
    • We use the symbol f (x) to represent the curve. f (x) is the function that corresponds to the graph; we use the density function f (x) to draw the graph of the probability distribution.
    • In general, calculus is needed to find the area under the curve for many probability density functions.

  • Two Types of Random Variables

    • The resulting probability distribution of the random variable can be described by a probability density, where the probability is found by taking the area under the curve.
    • The image shows the probability density function (pdf) of the normal distribution, also called Gaussian or "bell curve", the most important continuous random distribution.

  • Box-Cox Transformations

    • where $\Phi^{-1}$ is the inverse CDF of the normal density and x(i) denotes the ith sorted value of the data set.
    • The kernel density plot of the optimally transformed data is shown in the left frame of Figure 4.
    • (L) Density plot of the 1973 British income data.
    • (L) Density plot of the 1973 British income data transformed with λ = 0.21.

  • Distributions

    • They also carry the fancier name probability density.
    • Some probability densities have particular importance in statistics.
    • The Y-axis in the normal distribution represents the "density of probability. " Intuitively, it shows the chance of obtaining values near corresponding points on the X-axis.
    • Although this text does not discuss the concept of probability density in detail, you should keep the following ideas in mind about the curve that describes a continuous distribution (like the normal distribution).
    • For example, the normal probability density is higher in the middle compared to its two tails.