Reliability studies of the skew normal distribution

It has been observed in various practical applications that data do not conform to the normal distribution, which is symmetric with no skewness. The skew normal distribution proposed by Azzalini(1985) is appropriate for the analysis of data which is unimodal but exhibits some skewness. The skew normal distribution includes the normal distribution as a special case where the skewness parameter is zero. In this thesis, we study the structural properties of the skew normal distribution, with an emphasis on the reliability properties of the model. More specifically, we obtain the failure rate, the mean residual life function, and the reliability function of a skew normal random variable. We also compare it with the normal distribution with respect to certain stochastic orderings. Appropriate machinery is developed to obtain the reliability of a component when the strength and stress follow the skew normal distribution. Finally, IQ score data from Roberts (1988) is analyzed to illustrate the procedure.

Increasing Silicon Concentrations in Bohemian Forest Lakes

Long-term trends of dissolved silicon (Si) concentrations in five glacial lakes in the Bohemian Forest, Czech Republic, recovering from acidification show higher mobility of Si from the soil to surface waters despite lower atmospheric deposition of acids. Si increased by 0.95 to 1.95 mu mol yr(-1) (36 to 51%) from 1986-2004 and with increasing pH. A change in soil solution conditions because of a sharp decrease in acidic deposition has led to marked decline in Al mobility and to considerable decreases in dissolved Al, especially Al3+. The increase in Si may be related to: (1) unblocking of the inhibitory effect of dissolved Al on weathering of alummosilicates, (2) biogenic opal (phytoliths) dissolving faster, and/or (3) lower Si precipitation as secondary alummosilicates in soil. The change in Al speciation on the dissolution rate of biogenic silica is critical. A lack of change in Si at sites outside central Europe may be explained by small or no decline in mobility of dissolved Al. The effect of a long-term increase in temperature was probably minor.