llc: a collection of R functions for fitting a class of Lee-Carter mortality models using iterative fitting algorithms

We implement a specialised iterative regression methodology in R for the analysis of age-period mortality data based on a class of generalised Lee-Carter (LC) type modelling structures. The LC-based modelling frameworks is viewed in the current literature as among the most efficient and transparent methods of modelling and projecting mortality improvements. Thus, we make use of the modelling approach discussed in Renshaw and Haberman (2006), which extends the basic LC model and proposes to make use of a tailored iterative process to generate parameter estimates based on Poisson likelihood. Furthermore, building on this methodology we develop and implement a stratified LC model for the measurement of the additive effect on the log scale of an explanatory factor (other than age and time). This modelling methodology is implemented in a publically available collection of programming functions that facilitate both the preparation of mortality data and the fitting and analysis of the given log-linear modelling structures. Also, the package incorporates methods to produce forecasts of future mortality rates and to compute the corresponding future life expectancy

A comparative study of parametric mortality projection models

The relative merits of different parametric models for making life expectancy and annuity value predictions at both pensioner and adult ages are investigated. This study builds on current published research and considers recent model enhancements and the extent to which these enhancements address the deficiencies that have been identified of some of the models. The England & Wales male mortality experience is used to conduct detailed comparisons at pensioner ages, having first established a common basis for comparison across all models. The model comparison is then extended to include the England & Wales female experience and both the male and female USA mortality experiences over a wider age range, encompassing also the working ages

Investigation of electrical properties for cantilever-based piezoelectric energy harvester

In the present era, the renewable sources of energy, e.g., piezoelectric materials are in great demand. They play a vital role in the field of micro-electromechanical systems, e.g., sensors and actuators. The cantilever-based piezoelectric energy harvesters are very popular because of their high performance and utilization. In this research-work, an energy harvester model based on a cantilever beam with bimorph PZT-5A, having a substrate layer of structural steel, was presented. The proposed energy scavenging system, designed in COMSOL Multiphysics, was applied to analyze the electrical output as a function of excitation frequencies, load resistances and accelerations. Analytical modeling was employed to measure the output voltage and power under pre-defined conditions of acceleration and load resistance. Experimentation was also performed to determine the relationship between independent and output parameters. Energy harvester is capable of producing the maximum power of 1.16 mW at a resonant frequency of 71 Hz under 1g acceleration, having load resistance of 12 k Omega. It was observed that acceleration and output power are directly proportional to each other. Moreover, the investigation conveys that the experimental results are in good agreement with the numerical results. The maximum error obtained between the experimental and numerical investigation was found to equal 4.3%

The Transmuted Weibull-Pareto Distribution

A new generalization of the Weibull-Pareto distribution called the transmuted Weibull-Pareto distribution is proposed and studied. Various mathematical properties of this distribution including ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves and order statistics are derived. The method of maximum likelihood is used for estimating the model parameters. The flexibility of the new lifetime model is illustrated by means of an application to a real data set

A Study of Actuarial Models for Insurance Based Applications

Actuarial aspects of two important fields of insurance are considered: calculating personal injury damages for working age adults (liability insurance) and measuring the mortality in insurance based populations (e.g. life insurance and pensions). The contribution of the thesis is to demonstrate a wide array of modelling techniques and their practical implementation in these two key areas of actuarial science. The first part considers the modelling of the labour force dynamics from the perspective of the loss of earnings multipliers in England and Wales. It reviews the estimation methods of involuntary non{participation in the labour market in relation to future loss of earnings. In response, a robust multiple state modelling methodology is developed that allows conditioning on personal characteristics of working age individuals such as disability, educational attainment and the current employment state. Applied to UK longitudinal Labour Force Survey data, it quantifies the disadvantages that plaintiffs with post-injury earnings capacity face in the labour market. This practical modelling framework leads to a set of improved loss of earnings multipliers in subsequent editions of the Ogden Tables now used in the Courts in England and Wales. The second part focuses on the modelling and estimation of mortality rates using Poisson likelihood maximisation methods. In terms of graduation, it undertakes a comprehensive assessment of the frailty models and their implications. Then it puts forward suitable parametric modelling structures in order to measure the scale of individual heterogeneity and applies generalised linear modelling graduation techniques to a large array of insurance based mortality data. In terms of forecasting, it considers the generalised Lee-Carter type modelling structures of Renshaw and Haberman(2006) and demonstrates their suitability for practical applications.Furthermore, it develops a novel stratified Lee-Carter model for the measurement of the effects of explanatory factors (other than age and time). An efficient programming package in R is provided for this class of modelling framework. Finally, a detailed analysis of the mortality trends observed in private pension scheme data serves as a case study

2-Azido-1-(4-nitro­phen­yl)ethanone

In the title compound, C8H6N4O3, the ketone [C—C(=O)—C] and nitro groups are tilted with respect to the benzene ring by 18.92 (6) and 24.11 (15)°, respectively. In the crystal, mol­ecules are linked into inter­woven chains running parallel to the [100] direction by C—H⋯N hydrogen bonds and weak π–π stacking inter­actions, with centroid–centroid separations of 3.897 (3) Å