MY-ASSIGNMENTEXPERT™可以为您提供 lse.ac.uk ST227 Survival Models 生存模型的代写代考和辅导服务！
这是伦敦政经学院 生存模型课程的代写成功案例。
ST227课程简介
This course is compulsory on the BSc in Actuarial Science. This course is available on the BSc in Business Mathematics and Statistics, BSc in Data Science and BSc in Mathematics, Statistics and Business. This course is available as an outside option to students on other programmes where regulations permit and to General Course students.
Students must have completed Mathematical Methods (MA100) and Elementary Statistical Theory (ST102).
“Students must have completed one of the following two combinations of courses: (a) ST102 and MA100, or (b) MA107 and ST109 and EC1C1. Equivalent combinations may be accepted at the lecturer’s discretion.”
Prerequisites
An introduction to stochastic processes with emphasis on life history analysis and actuarial applications. Principles of modelling; model selection, calibration, and testing; Stochastic processes and their classification into different types by time space, state space, and distributional properties; construction of stochastic processes from finite-dimensional distributions, processes with independent increments, Poisson processes and renewal processes and their applications in general insurance and risk theory, Markov processes, Markov chains and their applications in life insurance and general insurance, extensions to more general intensity-driven processes, counting processes, semi-Markov processes, stationary distributions. Determining transition probabilities and other conditional probabilities and expected values; Integral expressions, Kolmogorov differential equations, numerical solutions, simulation techniques.
ST227 Survival Models HELP（EXAM HELP， ONLINE TUTOR）
If the survival function $S(t)=1-t / b$ for $0 \leq t \leq b$ for a fixed positive con-stant $b$, calculate the hazard function $h(t)$ for $0 \leq t \leq b$. Recall that $F(t)=1-S(t)$ and $f(t)$ is the derivative of $F$ with respect to $t$. By definition, $h(t)=f(t) / S(t)$. What is the lowest value for the hazard rate? Is there a highest val-ue for the hazard rate? Hint: Choose $M$ large. If there exists a $c<b$ such that $h(c)$ is greater than $M$ and $M$ is arbitrary, then there is no highest value for the hazard function.
Suppose the survival times (in months since transplant) for eight patients who received bone marrow transplants are $3.0,4.5,6.0,11.0,18.5,20.0,28.0$, and 36.0. Assume no censoring.
a. What is the median survival time?
b. What is the mean survival time?
c. Using 5 months as the interval, construct a life table for these data.
Again, we use the data from Exercise 15.5 , but we assume that $6.0,18.5$, and 28 are censor times.
a. Estimate the median survival time.
b. Why would an estimate of the mean survival time based on averaging all the times be inappropriate?
c. Using 5 months as an interval, construct a life table for the data.
15.8 Using the data in Exercise 15.7, construct a Kaplan-Meier estimate of the survival distribution.
15.9 Again using the data in Exercise 15.7, fit a negative exponential model. Compare it to the Kaplan-Meier curve at the event times 3, 4.5, 11.0, 20.0, and 36.0 months, and decide whether or not the negative exponential pro-vides a good fit.
15.10 Using a chi-square test, formally test the goodness of fit of the negative ex-ponential distribution obtained in Exercise 15.9. Test at the 0.05 level of sig-nificance.
15.11 Listed below in units of months are the survival and censor times (censoring denoted by a superscripted plus sign) for six males and six females.
Males: $1,3,4^{+}, 9,11,17$
Females: $1,3^{+}, 6,9,10,11^{+}$
a. Calculate a Kaplan-Meier curve for the males.
b. Calculate a Kaplan-Meier curve for the females.
c. Apply a chi-square test to determine if the two survival curves differ from one another.
MY-ASSIGNMENTEXPERT™可以为您提供 LSE.AC.UK ST227 SURVIVAL MODELS 生存模型的代写代考和辅导服务！
