Li (2000) introduced copula function approach in the aspect of evaluating credit derivatives, the copula function has gradually become the main approach in pricing CDO (Burtschell & George, 2005). In Li (2000) paper, a new random variable named ‘time-until-default’ was created to demonstrate survival time of each defaultable entity. And the copula function approach is based on this random variable to evaluate the default probability of financial instruments. Specifically, copula function specify the joint distribution of the survival times after using the market information to derive the marginal distribution of the survival time. This approach solves the default correlation and the joint distribution of the pool asset to some extent, and it…
a project which puts the cost at the top priority of the triple constrains, I would definitely use the EMV analysis to give my sponsors and other stakeholders a clear and valid risk analysis report. Finally, the third type of quantitative analysis and modeling techniques is the modeling and simulation, which means that one can translate the specified detailed uncertainties into future impact on project object (PMI, p. 340). Based on the research result, “Monte Carlo method is part of the…
Definition 1.1 A random forest is a classifier consisting of a collection of tree structured classifiers { , k=1, ...} where the are independent identically distributed random vectors and each tree casts a unit vote for the most popular class a input x . Use of the Strong Law of Large Numbers shows that they always converge so that overfitting is not a problem [] . The accuracy of a random forest depends on the strength of the individual tree classifiers and a measure of the dependence between…
In our every day lives we are faced with risk; the possibility of losing something of value. This could include theft or re to property, sickness, disability or even death. As loss adverse as we are, we tend to set up mediums to prevent or recover from losses once incurred. One of these common mediums is insurance. Anderson and Brown (2005) denes insurance as an agreement where, for a stipulated payment called the premium, one party (the insurer) agrees to pay to the other (the policyholder or…
The lottery is played all around the world. More than two-thirds of the citizens of the state. Anny three digit number can be placed from 000 to 999. After than the randomly draw a number. A number is drawn at random and announced by the state. The winner gets a prize. The probability that the correct 3 digits in the right order is selected is at an odds of 1 in 1,000. So if If a ticket costs two dollars and the winner must pick a sequence of five digits then if There are 10^5=100,000 different…
unit is a random selection of decline . In the simplest case , each unit is maintained…
In definition, probability refers to the measure of the likelihood of an event happening. The probability for any event occurring falls between 1 percent and 100 percent thus meaning that the interpreted meaning of a probability equals the subject meaning held of the probability (Grinstead et al, 1997). However, it is worth noting that the application of probability or assigning of probability to the events in the effort to gratifying the axioms of probability follows some rules or basics…
r 1,i and r 2,i are random values uniformly distributed over [0, 1]. This description of PSO is applicable to real-valued search spaces. However feature selection, along with many other problems, occur in a discrete search space and require a modified algorithm. Binary Particle Swarm Optimisation (BPSO) [?] is just such an algorithm. In BPSO, the values of the components of all position vectors (x i , pbest i , and gbest i ) are restricted to 0 or 1. Equation (2) is still used to update the…
푥푘+1; store 횪(푥푘+1) and the respective survivor 풙̂(푥푘+1) Set 푘 to 푘+1 and repeat until 푘=퐾. With finite state sequences 풙, the algorithm will terminate at time 퐾 with the shortest complete path stored as the survivor 풙̂(푥퐾). Fig. 3. Trellis diagram for a four-state shift register process. III. CONTINUOUS TIME MODEL We now evaluate the Viterbi algorithm under continuous time conditions, where the time index 풌 is a continuous random variable and we take 푘∈ℝ+. Thus, we have: (3) Pr(푋=푘)=푓(푘)=0 We…
trials, X, where X is a random variable has a negative binomial distribution with associated probability mass function given by; f_x (x│r,p)={█(((x-1)¦(r-1))@0 )┤ p^r (1-p)^(x-r) x=r,r+1,r+2,……, 0≤p≤1 Wheref_x (x│r,p) indicates that the function is dependent on r and p. (G. Casella, R. L. Berger, 2nd.Ed. 95) Considerably, the average number of successes per experiment of the random variable X with the negative binomial distribution indicates the ratio of the r^th success…