A bimodal distribution most commonly arises as a mixture of two different unimodal distributions ( i . e . distributions having only one mode ).
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Bimodal distributions have the peculiar property that unlike the unimodal distributions the mean may be a more robust sample estimator than the median.
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Conversely for a large class of unimodal distributions that are negatively skewed the mean is less than the median which in turn is less than the mode.
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Let " X " be a random variable with unimodal distribution, mean & mu; and finite, non-zero variance & sigma; 2.
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This results in a bimodal vibrational density profile that changes smoothly to a unimodal distribution as the well shallows, leading continuously into the vibrational density profile associated with a single well.
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The authors recommended a cut off value of 1.5 with B being greater than 1.5 for a bimodal distribution and less than 1.5 for a unimodal distribution.
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For a unimodal distribution, negative skew indicates that the " tail " on the left side of the probability density function is data might be transformed to have a normal distribution.
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The description of kurtosis as a measure of the " peakedness " ( or " heavy tails " ) of the probability distribution, is strictly applicable to unimodal distributions ( for example the normal distribution ).
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For dimension 3 I'd expect a uniform distribution on [-1, 1 ]-- cf Lambert cylindrical equal-area projection-- and increasingly narrow unimodal distribution for dimension 4 and above.
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In statistics, a "'unimodal probability distribution "'( or when referring to the distribution, a "'unimodal distribution "') is a probability distribution which has a single mode.
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