B
Filomena Pereira-Maxwell in Medical Statistics, 2018
As opposed to unimodal distribution. This term describes a variable whose distribution has two modes, i.e. two peaks. An example is shown in Figure B.3 (BINNIAN et al., 2016 - data from the US National Health and Nutrition Examination Survey or NHANES, 2011-2012), with the distribution of total urinary NNAL in a representative sample of the US population aged 6 years and over, which includes 4831 non-smokers and 961 cigarette smokers. NNAL is a major metabolite of the tobacco-specific nitrosamine carcinogen NNK, and was detected in 62.2% of non-smokers, and 99.8% of smokers. Values are on average higher for smokers than for non-smokers. As in this example, a bimodal distribution is often indicative of the presence in the sample of two distinct populations, with respect to the variable or characteristic being examined. Other examples could be blood glucose levels in a sample that includes diabetics and non-diabetics, or testosterone levels in a sample that includes males and females, for which each of the groups/populations has a distinct distribution, with a different average or measure of location, and sometimes also spreading over a wider or narrower range of values.
Some Statistical Procedures for Biomarker Measurements Subject to Instrumental Limitations
Albert Vexler, Alan D. Hutson, Xiwei Chen in Statistical Testing Strategies in the Health Sciences, 2017
Consider the problem of the estimation of the distribution function, FU, of a random variable U when observations from this distribution are contaminated by measurement error, that is, based on observations of random variables Y = U + ε, where ε represents measurement error. The estimation of FU has been referred to as deconvolution, since the distribution of each Yi is the convolution of the distributions of Ui and δi. Cordy and Thomas (1997) investigated the deconvolution of density by modeling the unknown distribution FU as a mixture of a finite number of known distributions. The mixture model was shown to be able to approximate a wide range of distributions. The authors also demonstrated that this approach can be applied to estimation of a unimodal distribution. In both models, parameters were estimated and large sample confidence intervals were constructed based on the well-known likelihood theory. Based on simulation studies, the good performance of the estimators and the confidence interval procedures were confirmed. The authors illustrated their methods by an application of data from a dietary survey reported by Clayton (1992), where the ratio of polyunsaturated to saturated fat intake (P/S) was measured for 336 males in a 1-week full-weighted dietary survey, and the authors considered the measured values of P/S for the ith individual as normally distributed with mean equal to the true value, UM, of P/S and constant measurement error variance.
Modeling of soybean yield using symmetric, asymmetric and bimodal distributions: implications for crop insurance
Published in Journal of Applied Statistics, 2018
Gislaine V. Duarte, Altemir Braga, Daniel L. Miquelluti, Vitor A. Ozaki
Figure 2 shows the density of the OLLN distribution for some values of the parameters α. It should be noted in the plots Figure 2(a, b) the contribution of the parameter α on the unimodality and bimodality of the distribution, when μ and σ are fixed. When the parameter α approaches zero, the pdf presents bimodality. On the other hand, when the value of α increases the function presents unimodality. It is observed that when μ varies, the plots is translated in the x-axis, regardless of the form Figure 2(c).
Modeling with a large class of unimodal multivariate distributions
Published in Journal of Applied Statistics, 2018
Another useful definition of unimodality is given by Devroye [7]: A multivariate density f on orthounimodal with mode at j,
A discrete analog of Gumbel distribution: properties, parameter estimation and applications
Published in Journal of Applied Statistics, 2021
Subrata Chakraborty, Dhrubajyoti Chakravarty, Josmar Mazucheli, Wesley Bertoli
A unimodal distribution is called strongly unimodal if its convolution with any other unimodal distribution is again unimodal. Strong unimodality implies unimodality. Some examples of strongly unimodal distributions are the Binomial and Poisson [20]. Strongly unimodal distribution, therefore, may have one (unique) or more modes.
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