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We study the problem of projecting a distribution onto (or finding a maximum likelihood distribution among) Markov networks of bounded tree-width.
For countries lacking sufficient vital registration data, cause of death models were used to firstly estimate the maximum likelihood distribution of deaths across the broad categories of communicable, non-communicable and injuries, based on estimated total mortality rates and income [ 8].
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This is equivalent to finding the maximum likelihood Gibbs distribution.
CFA was estimated using maximum likelihood and distribution free methods for comparison.
Figure 4 shows the fit of the maximum likelihood normal distribution to these data.
This was reflected in the near identical factor loadings obtained from maximum likelihood or distribution free estimation methods.
Assumptions about normality of scale items appeared to be justified by the almost identical parameter estimates of factor score loadings computed via maximum likelihood or distribution free methods.
Examining the 14 systems individually, they lie between the 28th and 81st percentiles in the maximum likelihood beta distribution of total coliform detects, suggesting that none of the study communities could be considered outliers with respect to drinking water sanitary quality.
To examine whether and how such interval-censored data influence our results, we performed sensitivity analyses using PROC LIFEREG, which fits a Weibull distribution to interval-censored lifetime data by maximum likelihood estimation of distribution parameters [ 45].
Using maximum likelihood, a lognormal distribution was fitted to these numbers.
It has been shown [ 13] that provided the distances derived from sequences satisfy the maximum likelihood criterion, their distribution is approximately multivariate normal, which allows to estimate their variances and covariances using the sample average method [ 13].
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