In a Stationary Population, the Average Lifespan of the Living Is a Length-Biased Life Expectancy

What is the average lifespan in a stationary population viewed at a single moment in time? Even though periods and cohorts are identical in a stationary population, we show that the answer to this question is not life expectancy but a length-biased version of life expectancy. That is, the distribution of lifespans of the people alive at a single moment is a self-weighted distribution of cohort lifespans, such that longer lifespans have proportionally greater representation. One implication is that if death rates are unchanging, the average lifespan of the current population always exceeds period life expectancy. This result connects stationary population lifespan measures to a well-developed body of statistical results; provides new intuition for established demographic results; generates new insights into the relationship between periods, cohorts, and prevalent cohorts; and offers a framework for thinking about mortality selection more broadly than the concept of demographic frailty.

Are Roundabouts Safe and Economically Viable Replacing Conventional Diamond Interchange Ramp Terminals?

Roundabout implementations at traditional intersections have been shown to be effective at reducing severe crashes. Roundabouts have also been implemented at interchange ramp terminals; however, limited research is available. In this study, 25 roundabout ramp terminal implementations were evaluated. The methodological approach consisted of Empirical Bayes for safety effectiveness and crash cost changes, crash type weighted distribution, crash rate analysis of bypass configuration, and cost of implementation. Roundabouts were effective at reducing fatal and injury crashes when replacing existing interchange diamond ramp terminals: 65% reduction for roundabouts replacing stop-controlled ramp terminals and 41% reduction for roundabouts replacing signal-controlled ramp terminals. Observed crash type weighted distributions are provided to visualize the frequency and location of crashes within roundabout ramp terminals for design considerations. Exit ramp and outside crossroad approaches with right-turn bypass showed significantly lower crash rates than designs without bypass. The crash cost analysis showed that roundabouts replacing diamond ramp terminals yielded crash cost savings of between $95,000 and $253,000 per site per year (69% to 54% decrease in crash costs). Considering crash costs savings only, the cost of implementation should be less than $1.9 million for a roundabout replacing a stop-controlled ramp terminal and less than $5.1 million for a roundabout replacing a signal-controlled ramp terminal to accomplish benefit-cost ratios greater than one for a service life cycle of 20 years. Costs are in 2019 dollars.

Comparing methods to estimate the proportion of turbine-induced bird and bat mortality in the search area under a road and pad search protocol

Estimating bird and bat mortality at wind facilities typically involves searching for carcasses on the ground near turbines. Some fraction of carcasses inevitably lie outside the search plots, and accurate mortality estimation requires accounting for those carcasses using models to extrapolate from searched to unsearched areas. Such models should account for variation in carcass density with distance, and ideally also for variation with direction (anisotropy). We compare five methods of accounting for carcasses that land outside the searched area (ratio, weighted distribution, non-parametric, and two generalized linear models (glm)) by simulating spatial arrival patterns and the detection process to mimic observations which result from surveying only, or primarily, roads and pads (R&P) and applying the five methods. Simulations vary R&P configurations, spatial carcass distributions (isotropic and anisotropic), and per turbine fatality rates. Our results suggest that the ratio method is less accurate with higher variation relative to the other four methods which all perform similarly under isotropy. All methods were biased under anisotropy; however, including direction covariates in the glm method substantially reduced bias. In addition to comparing methods of accounting for unsearched areas, we suggest a semiparametric bootstrap to produce confidence-based bounds for the proportion of carcasses that land in the searched area.

Enhancement and Segmentation of Medical Images Using AGCWD and ORACM

<p>Images that are obtained in the real world in low contrast are inappropriate for human eyes to read the medical images. Enhancement and segmentation have an important role to play in digital image processing, pattern recognition, and the computer vision. Here, this paper presents an effective way of changing histograms and improving contrast in digital images. Segmentation is done on AGCWD enhanced images. Histogram equalization is an important technique for contrast enhancement. Nevertheless, modern Histogram Equalization commonly results in unnecessary contrast enhancement, which in turn offers an un-natural presence to the processed image and produces visual artifacts. We present an automated transformation technique that helps boost dimmed image brightness by gamma correction and weighted distribution, commonly known as Adaptive Gamma Correction Weighted Distribution (AGCWD). The contrast enhancement level can be modified using this technique; noise robustness, white or black stretching, and the protection of medium brightness can be easily integrated into the optimization process. Finally, a contrast enhancement algorithm with low complexity is introduced. All the process of enhancement will be done during the process of pre-processing the image. Later, in post-processing, we introduce a specific level set method known as ORACM for better segmentation of an enhanced AGCWD image, and it is compared with the traditional level set method.</p>

Some Statistical Properties of a Weighted Distribution and Its Application to Waiting Time Data

The weighted distribution is mainly used in various real life fields such as ecology, reliability engineering, medical science etc. Some statistical properties are derived such as moment generating function, characteristic function, cumulative generating function, the hazard function, Renyi entropy, Cumulative residual entropy. For parameter estimation maximum likelihood estimation method is used. The considered weighted probability distribution is applied to two real data sets of waiting time to examine the suitability and applicability.