We give necessary and sufficient conditions for a scoring rule to be proper (or strictly proper) for a quantile if utility is linear, and the distribution is unrestricted. We also give results when the set of distributions is limited, for example, to distributions that have first moments.

We study the distribution of discounted collective risk model where the counting process is Poisson. For the model considered here, we obtain mean, variance and moment generating function (m.g.f) of the model. To do this, we use two approaches. In the first approach we use classical methods to obtain the mean and variance. In the second approach we introduce some proper martingale and then we o...

Proper planning of assembly lines is one of the production managers’ concerns at the tactical level so that it would be possible to use the machine capacity, reduce operating costs and deliver customer orders on time. The lack of an efficient method in balancing assembly line can create threatening problems for manufacturing organizations. The use of assembly line balancing methods cannot balan...

The binomial moments of a linear code are synonymously related to its weight distribution and appear naturally in studies involving the weight distribution of the code. In particular , the binomial moments have been used for establishing bounds on the undetected error probability and, though implicitly, for the study of good and proper codes. In this work we sharpen known bounds on the binomial...

Synaptic remodelling coordinated with dendritic growth is essential for proper development of neural connections. After establishment of synaptic contacts, synaptic junctions are thought to become stationary and provide fixed anchoring points for further dendritic growth. However, the possibility of active translocation of synapses along dendritic protrusions, to guide the proper arrangement of...

This article discusses a family of distributions which would seem not to receive proper attention in the literature. The twoparameter distribution is introduced with an application in the financial engineering domain. Special cases of this family include the triangular distribution, the standard power function distribution, and the uniform distribution. Properties of the distribution are invest...