These rates were multiplied by the reference age distribution and summed to form age-adjusted totals.
In fact, the distribution of pause durations can be derived exactly from this model by calculating the probability of observing a random trajectory with n steps, multiplying it by the distribution of times that it takes to perform those steps (which is given by a Gamma distribution), and summing over all allowed values of n.
Special cases include the exponential distribution, and the sum of identical independent exponentials.
We multiplied the model contribution by 2 so that our best estimate gave equal weight to the a priori atmospheric model distribution and the sum of the two satellite-scaled estimates.
For μ≥3, there is no heavy tail in the distribution and the sums of the flight lengths converge to a Gaussian distribution due to the Central Limit Theorem, thus we recover Brownian walks.
Similarly, crosstalk models based on beta distribution [24] and sum-of-sinusoids [25] have been suggested to characterize the crosstalk accurately.
Moreover, Wu [12 14] explored the almost sure limit theorem for product of partial sums, stable distribution and product of sums of partial sums, respectively.
For simple comparison analysis, Student's t test was performed to compare parametric distribution and Mann Whitney rank sum tests were performed to compare non-parametric distribution.
Mismatch distribution analyses rejected the range expansion hypothesis for this group by a bimodal distribution and significant SSD (sum of square deviations) and RAG (Harpending's raggedness index) values.
For BubR1 and Aurora A, the results for intensity and distribution were summed and total score was assigned as follows: sum of 0 1, score 0; sum of 2 3, score 1; sum of 4 5, score 2; sum of 6 7, score 3. The relationships between categorical variables were assessed using the χ test.
