Stochastic estimation of the distribution of soil water repellency on the soil surface in a humid-temperate forest

Soil water repellency (SWR) increases surface runoff and preferential flows. Thus, quantitative evaluation of SWR distribution is necessary to understand water movements. Because the variability of SWR distribution makes it difficult to measure directly, we developed a method for estimating an SWR distribution index, defined as the areal fraction of surface soil showing SWR (SWRarea). The theoretical basis of the method is as follows: (1) SWRarea is equivalent to the probability that a position on the soil surface is drier than the critical water content (CWC); SWR is present (droplets absorbed in >10 s) when the soil surface is drier than the CWC and absent when it is wetter. (2) CWC and soil moisture content (θ) are normally distributed independent variables. (3) Thus, based on probability theory, the cumulative normal distribution of θ – CWC (f(x)) can be obtained from the distributions of CWC and θ, and f(0), the cumulative probability that θ – CWC < 0, gives the SWRarea. To investigate whether the method gives reasonable results, we repeatedly measured θ at 0–5 cm depth and determined the water repellency of the soil surface at multiple points in fixed plots with different soils and topography in a humid-temperate forest. We then calculated the CWC from the observed θ–SWR relationship at each point. We tested the normality of the CWC and θ distributions and the correlation between CWC and θ. Then, we determined f(x) from the CWC and θ distributions and estimated the SWRarea on each measurement day. Although CWC and θ were both normally distributed, in many cases they were correlated. Nevertheless, the CWC–θ dependency had little effect on the estimation error, and f(x) explained 69% of the SWRarea variability. Our findings show that a stochastic approach is useful for estimating SWRarea.

PSII-8 Defining pig sort loss with a simulation of various marketing options of pigs with the assumption that marketing cuts improve variation in carcass weight and leanness

The study offers clarification on pig sort loss and associated marketing strategies using a simulated pig marketing modeling system. The objective was to investigate the economic variability associated with marketing strategies using the simulated pig marketing models. Typically, individual pigs are assessed by measuring carcass weight and predicted leanness, which is then incorporated into a two-factor grid for producer payment, providing incentives for producers who consistently produce desirable carcasses and discounts for producers who produce inconsistent or undesirable carcasses. The simulation considered six producers with the presumption that each had a maximum capacity for 4,800 grow-finish pigs, in order to imitate commercial finishing barns with 48 pens of roughly 100 pigs per pen. The simulation dataset was created using a random number generator with the inverse of the cumulative normal distribution function on Microsoft Excel (Microsoft Inc., USA) with a targeted carcass weight (102.86 kg) and average predicted lean (60%) based on industry averages and previous research studies. Under the assumption that variability in carcass weight and predicted leanness decreased with the addition of each marketing cut, the simulation incorporated a standard deviation reduction of 20% per increase of one marketing cut for both carcass weight and predicted leanness of the population of pigs marketed on a given day. Consequently, there was an increase in profitability; as well as, a decrease in pig sort loss (defined with both carcass weight and predicted leanness) with each marketing cut, but these profitability improvements diminished (as a percentage improvement) with each additional marketing cut. Finally, this simulation provides an appropriate framework and the necessary equations to allow repetition of the different parameters and marketing grid specifically related to an individual producer and processing facility. Thus, helping the industry gain a better understanding of how market cuts can decrease variation and consequently improve profitability.

Evaluation of Liquefaction Potential for Large Areas Based on Geomorphologic Classification

Ground motion maps and observation records of liquefaction sites from ten historical earthquakes are used to develop predictive equations for the regional occurrence of liquefaction. Liquefaction occurrence ratio is determined for different geomorphological conditions and intervals of causative shaking intensity obtained from the observation data. Probability regression analysis of these data, based on a cumulative normal distribution, is then used to develop equations for estimating probability of liquefaction for different geomorphological conditions given shaking intensity. Utility of the model is demonstrated for a hypothetical Tonankai-Nankai earthquake to create an estimated liquefaction potential map having 250-m grid-cells. The approach shows promise for rapid online generation of liquefaction maps following an earthquake.

Reasons of Tax Avoidance and Tax Evasion: Reflections from Pakistan

Amount of taxes serves as life blood for government. This paper aims to recognize reasons/causes of tax avoidance and evasion in Pakistan. Relationship between variables of reasons/causes of tax avoidance and evasion are also examined. A questionnaire is developed after reviewing literature to collect responses. Data are analyzed using percentages, arithmetic mean, standard deviation, variance, central limit theorem, cumulative normal distribution calculator, factor analysis, and correlation technique. Results indicate that all variables of reasons/causes of tax avoidance and evasion in Pakistan are correct. Furthermore, there exists a highly significant positive relationship between individual variables of reasons/causes of tax avoidance and evasion in Pakistan at 100% significance level.

Essentially exact asymptotic solutions for Asian derivatives

In this paper, we will show how to obtain asymptotic solutions for the problem of pricing Asian options. Under the assumption that the underlying follows geometric Brownian motion, we will derive Taylor expansion series for the fixed and floating strike Asian options. While there will be no analytical formulae for calculating expansion coefficients, we will provide relatively simple algorithms for calculating them. The methodology is particularly effective for the case of continuously sampled fixed-strike Asian calls where it takes only seconds to obtain constants for the Taylor expansion series that can converge beyond 10 significant digits. It is needless to say that we need to calculate Taylor expansion constants only once and the option price would be an analytical expression constructed from a cumulative normal distribution function, an exponential function and finite sums.