Academic literature on the topic 'Non central chi-square distribution function'

An integral part of the transition from ‘huts’ to ‘houses’ in the seventh and early sixth century BC was the adoption of a new roofing system using wooden beams and terracotta tiles instead of traditional thatch. The two elements of the new system formed an integrated unit, with special tiles designed and positioned to protect the perishable wooden beams from rain, wind, and fire; many also carried painted and moulded decorations that have encouraged study of their iconography as well as function. The disappearance of wooden trusses and supporting mud-brick walls from the archaeological record means that thousands of these durable tiles and architectural terracottas now comprise the primary evidence for the size, form, and decoration of many early Etruscan and Latial superstructures. Excavations in the last seventy years have yielded new information about the distribution of the decorative elements of these roofs in Etruria and Latium, and in particular about the different types of buildings on which they appeared. It is clear that architectural terracottas were initially placed on a wide variety of buildings, unlike their Greek counterparts, but gradually became the preserve of religious architecture. This chapter will examine the nature and location of these roofs, their imagery, and explanations for their increasingly limited use. As such it will offer a detailed analysis of the process by which terracottas became a means of differentiating religious buildings from vernacular architecture during the sixth century BC. Tile production appears to have begun in central Italy by the middle of the seventh century BC and can be associated with significant changes in society and economy. With an approximate weight of 60 kilograms per square metre for tiles and up to 85 kilograms per square metre for the supporting roof beams, the downward and outward pressure of tiled roofs had to be countered with strong, preferably stonebased, walls following rectangular or square plans, the careful selection of timbers to span greater distances, and specialized craftsmen to make, fit, and repair the roofs. All of these factors imply more sedentary communities than hut architecture, growing technical infrastructure, and an ability and readiness to invest in the greater capital expense of a tiled roof.

This paper proposes a novel second-order reliability method (SORM) using non-central or general chi-squared distribution to improve the accuracy of reliability analysis in existing SORM. Conventional SORM contains three types of errors: (1) error due to approximating a general nonlinear limit state function by a quadratic function at most probable point (MPP) in the standard normal U-space, (2) error due to approximating the quadratic function in U-space by a hyperbolic surface, and (3) error due to calculation of the probability of failure after making the previous two approximations. The pro