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Variant: kernel density estimation

A method for the estimation of probability density functions. Suppose X is a continuous random variable with unknown probability density function f. A random sample of observations of X is taken. If the sample values are denoted by x₁, x₂,..., x_n, the estimate of f is given by

where K is a kernel function and the constant A is chosen so that


The observation x_j may be regarded as being spread out between x_j − a and x_j+b (usually with a=b). The result is that the naive estimate of f as being a function capable of taking values only at x₁, x₂,..., x_n, is replaced by a continuous function having peaks where the data are densest. Examples of kernel functions are the Gaussian kernel,


and the Epanechikov kernel,


, The constant h is the window width or bandwidth. The choice of h is critical: small values may retain the spikes of the naive estimate, and large values may oversmooth so that important aspects of f are lost.


Kernel method. In this case a sample of twenty observations have been generated randomly from a chi-squared distribution with twenty degrees of freedom and a Gaussian kernel with h=3 has been used to generate the kernel density estimate.
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In radio astronomy, the range of frequencies occupied by a signal or to which a detector is sensitive.

For more information on bandwidth, visit Britannica.com.

1. [common] Used by hackers (in a generalization of its technical meaning) as the volume of information per unit time that a computer, person, or transmission medium can handle. “Those are amazing graphics, but I missed some of the detail — not enough bandwidth, I guess.” Compare low-bandwidth; see also brainwidth. This generalized usage began to go mainstream after the Internet population explosion of 1993-1994.

2. Attention span.

3. On Usenet, a measure of network capacity that is often wasted by people complaining about how items posted by others are a waste of bandwidth.

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The data transfer capacity of a network. It is measured in bits per second.

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Width of the band of frequencies between the half power points.

(DOD) The difference between the limiting frequencies of a continuous frequency band expressed in hertz (cycles per second). The term bandwidth is also loosely used to refer to the rate at which data can be transmitted over a given communications circuit. In the latter usage, bandwidth is usually expressed in either kilobits per second or megabits per second.

i. The range of frequencies, above and/or below the frequency of a carrier wave, required for modulation of a signal. It is the width of the transmitted frequency spectrum (the difference between the highest and the lowest frequency) of a modulated signal.



ii. A band of error, usually expressed in nautical miles on each side of the position line on the track. See band of error.
iii. The range of frequencies between which an aerial performs to the specified standard.
iv. The space in the frequency domain occupied by signals of a specified nature (e.g., radar, TV).
v. The number of cycles per second between the limits of a frequency band.
vi. In information theory, the information-carrying capacity of a communications channel.

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For a list of words related to bandwidth, see:

• Data Transmission - bandwidth: smallest range of frequencies within which certain signal can be transmitted

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See words rhyming with "bandwidth."

This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)

Common misspelling(s) of bandwidth

• bandwith

Dansk (Danish)
n. - båndbredde

Français (French)
n. - (Comput) largeur de bandes

Deutsch (German)
n. - Bandbreite

Ελληνική (Greek)
n. - ραδιοφωνική συχνότητα, εύρος ζώνης (δεδομένα που μεταδίδονται ανά δευτερόλεπτο)

Español (Spanish)
n. - anchura de la banda, (informática) cantidad de información, rango de frecuencias

Svenska (Swedish)
n. - bandbredd, frekvensområde, datamängd

中文（简体）(Chinese (Simplified))
带宽, 频宽

中文（繁體）(Chinese (Traditional))
n. - 帶寬, 頻寬

한국어 (Korean)
n. - 띠폭(주파수 폭)

العربيه (Arabic)
‏(الاسم) مدى الترددات ( راديو), كميه البيانات ( كومبيوتر)‏

עברית (Hebrew)
n. - ‮רצועת התדירויות הצרה ביותר בה ניתן לשדר סימן מסוים ללא שיבושים‬

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