We elicit social networks among students in an Italian high school either by measuring the complete network in an incentive-compatible way or by using a truncated elicitation of at most five links. We find that truncation undercounts weak links by up to 90% but only moderately undercounts the time spent with strong friends. We use simulations to demonstrate that the measurement error induced by censoring might be particularly significant when studying phenomena such as social learning which are often thought to operate along weak ties. We then discuss how a modified network elicitation protocol might be able to reduce measurement error.

Most of the previous research examined the demand for alcohol consumed at the off-trade (consumed at home). However, some consumers might prefer to consume alcohol on-trade (away from home) or switch between on-trade and off-trade consumption as a reaction to price or income change. We estimate the Quadratic Almost Ideal Demand System consisting of three broad alcohol categories, consumed on-trade and off-trade, to derive own-price, cross-price, and income elasticities. Selectivity due to the high censoring is treated, and special attention is paid to quality-adjusted price. Beer consumption is the most responsive to income as well as own price changes, while spirits are the least responsive. The own-price elasticity of wine is –0.66 and –1.00 at on-trade and off-trade, respectively. Beer is more price responsive, spirits are less price responsive, and consumption reacts weaker in the off-trade market. Own-price elasticities of demand range between –1.20 and –0.41 at the off-trade and between –1.51 and –0.63 at the on-trade alcohol market. Increasing the price of wine in one market decreases wine consumption in another one. Between the two markets, wine and spirits are complementary, and wine and beer are substitutes in both markets.

Determining the germination speed is essential in experiments in the field of seed technology, as it allows the performance evaluation of a seed lot and the creation of predictive models. To this end, the literature addresses several methods and indexes. The objective of this study was to compare the main methods of emergence speed analysis in seeds, namely the non-linear regression models and the Emergence Speed Index (ESI), with the time-to-event models. The research was conducted with peach palm seeds (Bactris gasipaes) that were measured for viability and vigour through daily evaluations for 4 months. Vigour was evaluated by the quantification of the seed emergence speed, which was performed in three ways: ESI, non-linear regression and non-linear regression considering germination as a time-to-event event. From the results obtained, we conclude that the ESI is not a good indicator to evaluate the emergence speed; the non-linear regression model underestimates the errors and, thus, increases the probability of misclassifying treatments; the time-to-event model is more reliable in classifying treatments according to the emergence speed.

Pre-weaning animals exit a flock through death induced by various reasons, causing significant economic losses to the goat producers. In this study, we investigated the survival from birth to weaning of Sirohi goat kids within framework of the survival analysis. Kid records were accessed from 1997 to 2017, with the information on 4417 pre-weaning animals of farmed Sirohi goat native to the Rajasthan State of India. A multivariable Cox regression was fitted to the data after checking the assumptions of regression. The explanatory variables were sex, type of birth, season of birth, birthweight, doe weight at kidding and year of birth. Model selection eliminated doe weight from the model, and sex, type of birth, season of birth, birthweight and year of birth were retained in the model. With model calibration also, these five covariates were retained in the model. The mortality on the first day after birth was 0.3%, constituting 3.5% of all pre-weaning mortality. The mortality until the end of weaning period was 7.8%. Regression analysis revealed that the higher birthweight at kidding was associated with reduced hazard of death among the kids. Male kids had higher hazards of death compared with female kids. The single-born kids had lower risks of death compared with twin-born kids after accounting for heterogeneity. The winter season had a very high adverse effect on the survival of the kids. With each passing year, risks of death decreased. The results of this study indicate that better survival of kids can be achieved by controlling both environmental and animal-related factors.

In non-life insurance, business sustainability requires accurate and robust predictions of reserves related to unpaid claims. To this aim, two different approaches have historically been developed: aggregated loss triangles and individual claim reserving. The former has reached operational great success in the past decades, whereas the use of the latter still remains limited. Through two illustrative examples and introducing an appropriate tree-based algorithm, we show that individual claim reserving can be really promising, especially in the context of long-term risks.

Factors associated with purchase likelihoods and amounts spent on fresh and preserved vegetables in Malaysia are investigated. A sample selection system is applied to data from a national survey in Malaysia. Statistical test supports separate analyses for urban and rural households. Income and sociodemographic characteristics such as ethnicity, location of residence, household size, and education are closely associated with household expenditure patterns of fresh and preserved vegetables. Urban-rural differences are also uncovered in these effects. Several observations are noted vis-à-vis the expenditure patterns for fresh and preserved vegetables in Malaysia.

A sample selection system is used to examine factors associated with likelihoods of purchase and amounts spent on fresh, frozen, and processed meats in Malaysia based on data from the 2009/10 Malaysian Household Expenditure Survey. Statistical tests support use of the sample selection system estimator over more conventional estimation procedures. Results indicate that household size, location of residence, ethnicity, age, education, and income are closely associated with patterns of household expenditures for fresh, frozen, and processed meats. Several observations are noted regarding determinants of purchase likelihoods and expenditure patterns for meat in Malaysia.

We discuss how to fit mixtures of Erlangs to censored and truncated data by iteratively using the EM algorithm. Mixtures of Erlangs form a very versatile, yet analytically tractable, class of distributions making them suitable for loss modeling purposes. The effectiveness of the proposed algorithm is demonstrated on simulated data as well as real data sets.

This article examines the impact of Bt corn adoption in the Philippines using an econometric approach that addresses simultaneity, selection, and censoring problems. Although previous literature emphasizes the importance of simultaneity and selection problems, this is the first study that addresses the issue of censoring in estimating the effects of Bt corn adoption at the farm in a developing country context. We show that Bt corn adoption provides modest but statistically significant increases in farm yields and profits. Furthermore, our results provide some evidence of inference errors that can potentially arise when censoring in the pesticide application variable is ignored in the estimation procedures.

Many studies that gather social network data use survey methods that lead to censored, missing, or otherwise incomplete information. For example, the popular fixed rank nomination (FRN) scheme, often used in studies of schools and businesses, asks study participants to nominate and rank at most a small number of contacts or friends, leaving the existence of other relations uncertain. However, most statistical models are formulated in terms of completely observed binary networks. Statistical analyses of FRN data with such models ignore the censored and ranked nature of the data and could potentially result in misleading statistical inference. To investigate this possibility, we compare Bayesian parameter estimates obtained from a likelihood for complete binary networks with those obtained from likelihoods that are derived from the FRN scheme, and therefore accommodate the ranked and censored nature of the data. We show analytically and via simulation that the binary likelihood can provide misleading inference, particularly for certain model parameters that relate network ties to characteristics of individuals and pairs of individuals. We also compare these different likelihoods in a data analysis of several adolescent social networks. For some of these networks, the parameter estimates from the binary and FRN likelihoods lead to different conclusions, indicating the importance of analyzing FRN data with a method that accounts for the FRN survey design.

This paper surveys some statistical models of survival data. A basic model of a random lifetime is defined, and censoring is introduced. Methods based on observations of small segments of lifetimes are compared. Markov and semi-Markov (multiple state) models are recommended as well-understood and flexible models well suited to actuarial data. A Poisson model is discussed as an approximation to a two state model, while traditional Binomial-type models are shown to be more restricted and less tractable than multiple state models.

Counting processes and their compensators are introduced at a heuristic level. The martingale property of stochastic integrals with respect to a compensated counting process leads to moment estimates and asymptotic normal distributions for statistics arising in multiple state, non-parametric and semi-parametric models. The place of survival models in actuarial education is discussed.

We consider a failure hazard function,conditional on a time-independent covariate Z,given by $\eta_{\gamma^0}(t)f_{\beta^0}(Z)$ . The baseline hazardfunction $\eta_{\gamma^0}$ and the relative risk $f_{\beta^0}$ both belong to parametricfamilies with $\theta^0=(\beta^0,\gamma^0)^\top\in \mathbb{R}^{m+p}$ . The covariate Z has an unknown density and is measured with an error through anadditive error model U = Z + ε where ε is a random variable, independent from Z, withknown density $f_\varepsilon$ .We observe a n-sample (Xi, Di, Ui), i = 1, ..., n, where X i isthe minimum between the failure time and the censoring time,and D i is the censoring indicator.Using least square criterion and deconvolution methods, we propose a consistent estimator of θ 0 using the observationsn-sample (Xi, Di, Ui), i = 1, ..., n.
We give an upper bound for its riskwhich depends on the smoothness properties of $f_\varepsilon$ and $f_\beta(z)$ as afunction of z, and we derive sufficient conditionsfor the $\sqrt{n}$ -consistency.We give detailed examples consideringvarious type of relative risks $f_{\beta}$ and various types of errordensity $f_\varepsilon$ . In particular, in the Cox model and inthe excess risk model, the estimator of θ 0 is $\sqrt{n}$ -consistent and asymptotically Gaussianregardless of the form of $f_\varepsilon$ .

In this paper we consider discrete-time multidimensional Markov chains having a block transition probability matrix which is the sum of a matrix with repeating block rows and a matrix of upper-Hessenberg, quasi-Toeplitz structure. We derive sufficient conditions for the existence of the stationary distribution, and outline two algorithms for calculating the stationary distribution.

We apply Lemaire's algorithm and a non-parametric mixed Poisson fit to a motor insurance portfolio in order to find the true claim frequency and claim amount distributions. The algorithm we develop accounts for the fact that observed distributions are distorted by bonus hunger, when a bonus-malus system is used by the insurer.

The calculation of mean claim sizes, in the presence of a deductible, is usually achieved through numerical integration. In case of a Lognormal or Gamma distribution, the quantities of interest can easily be expressed as functions of the cumulative distribution function, with modified parameters. This also applies to the F-distribution, where the incomplete Beta function enters the scene; see for instance the appendix in Hogg and Klugman (1984).

The purpose of this paper is to derive an explicit formula for the first two moments of the Inverse Gaussian distribution, in the presence of censoring. For reasons of completeness we also consider truncation of the Inverse Gaussian distribution by an upper limit.

The tractability of the derivation depends in a crucial way on two properties of the Inverse Gaussian distribution. Firstly, the cumulative distribution function of the Inverse Gaussian can be written as a simple function using the Normal probability integral. Secondly, the moment generating function of a censorized Inverse Gaussian distribution boils down to an expression containing the cumulative Inverse Gaussian distribution. This manifests itself most clearly in case of life insurance where the quantity of interest is the expectation of a present value. In case of non-life insurance, where the dimension of the Inverse Gaussian random variable is money instead of time, a further step is required: differentiation of the moment generating function.

So, a natural order of this paper is to address ourselves first to the derivation for the life case and afterwards tackling the more laborious derivation for the non-life case.