Log-concavity of compound distributions with applications in operational and actuarial models

We establish that a random sum of independent and identically distributed (i.i.d.) random quantities has a log-concave cumulative distribution function (cdf) if (i) the random number of terms in the sum has a log-concave probability mass function (pmf) and (ii) the distribution of the i.i.d. terms has a non-increasing density function (when continuous) or a non-increasing pmf (when discrete). We illustrate the usefulness of this result using a standard actuarial risk model and a replacement model.We apply this fundamental result to establish that a compound renewal process observed during a random time interval has a log-concave cdf if the observation time interval and the inter-renewal time distribution have log-concave densities, while the compounding distribution has a decreasing density or pmf. We use this second result to establish the optimality of a so-called (s, S) policy for various inventory models with a stock-out cost coefficient of dimension [$/unit], significantly generalizing the conditions for the demand and leadtime processes, in conjunction with the cost structure in these models. We also identify the implications of our results for various algorithmic approaches to compute optimal policy parameters. Copyrigh

Generalized models of repairable systems: A survey via stochastic processes formalism

In this article, we survey the developments in the generalised models of repairable systems reliability during 1990s, particularly the last five years. In this field, we notice the sharp fundamental problem that voluminous complex models were developed but there is an absence of sufficient data of interest for justifying the success in tackling the real engineering problems. Instead of following the myth of using simple models to face the complex reality, we select and review some practical models, particularly the stochastic processes behind them. The Models in three quick growth areas: age models, condition monitoring technique related models, say, proportional intensity and their extensions, and shock and wearing models, including the delay-time models are reviewed. With the belief that only those stochastic processes reflecting the instinct nature of the actual physical processes of repairable systems, without excessive assumptions, may have a better chance to meet the demands of engineers and managers

Inspection and replacement models for reliability and maintenance: filling in gaps

A thesis submitted in fulfillment of the requirements for the Degree of Doctor of Philosophy, School of Statistics and Actuarial Science, Faculty of Science University of Witwatersrand, Johannesburg. February 2017.The work done in this thesis on finite planning horizon inspection models has demonstrated that with the advent of powerful computers these days it is possible to easily find an optimal inspection schedule when the lifetime distribution is known. For the case of system time to failure following a uniform distribution, a result for the maximum number of inspections for the finite planning models has been derived. If the time to failure follows an exponential distribution, it has been noted that periodically carrying out inspections may not result in maximization of expected profit. For the Weibull distributions family (of which the exponential distribution is a special case), evenly spreading the inspections over a given finite planning horizon may not lead to any serious prejudice in profit. The case of inspection models where inspections are of non-negligible duration has also been explored. The conditions necessary for inspections that are evenly spread over the entire planning horizon to be near-optimal when system time to failure either follows a uniform distribution or exponential distribution have been explored. Finite and infinite planning horizon models where inspections are imperfect have been researched on. Interesting observations on the impact of Type I and Type II errors in inspection have been made. These observations are listed on page 174. A clear and easy to implement road map on how to get an optimal inspection permutation in problems first discussed by Zuckerman (1989) and later reviewed by Qiu (1991) for both the undiscounted and discounted cases has been given. The only challenge envisaged when a system has a large number of components is that of computer memory requirements - which nowadays is fast being overcome. In particular, it has been clearly demonstrated that the impact of repair times and per unit of time repair costs on the optimal inspection permutation cannot be ignored. The ideas and procedures of determining optimal inspection permutations which have been developed in this thesis will no doubt lead to huge cost savings especially for systems where the cost of inspecting components is huge.XL201

Correlated observations, the law of small numbers and bank runs

Empirical descriptions and studies suggest that generally depositors observe a sample of previous decisions before deciding if to keep their funds deposited or to withdraw them. These observed decisions may exhibit different degrees of correlation across depositors. In our model depositors decide sequentially and are assumed to follow the law of small numbers in the sense that they believe that a bank run is underway if the number of observed withdrawals in their sample is large. Theoretically, with highly correlated samples and infinite depositors runs occur with certainty, while with random samples it needs not be the case, as for many parameter settings the likelihood of bank runs is zero. We investigate the intermediate cases and find that i) decreasing the correlation and ii) increasing the sample size reduces the likelihood of bank runs, ceteris paribus. Interestingly, the multiplicity of equilibria, a feature of the canonical Diamond-Dybvig model that we use also, disappears almost completely in our setup. Our results have relevant policy implications

Molecular manipulation and new antimicrobial identification in Acanthamoeba spp

Date on title page is date of submission (November 2021). Date of award is 2022.Acanthamoeba spp. are causative agents of a painful and severe sight-threatening corneal infection that can lead to blindness known as Acanthamoeba keratitis and a subacute disease in the brain which is usually fatal known as granulomatous amoebic encephalitis. Over the last few years, there has been a notorious increase in the number of infections due to Acanthamoeba spp. Poor diagnosis, problems of side effects, toxicity of the current drug treatment and the lack of gene editing tools as potential future therapy contribute to a high mortality rate. Strathclyde Minor Groove Binders (S-MGBs), compounds that bind to the minor groove of the DNA that designed and synthesised at University of Strathclyde were evaluated as potential alternative inhibitors against Acanthamoeba infections. Through cell viability microplate alamarBlue assays 42 S-MGBs were screened from which S-MGB 235 showed the most potent inhibitory effect with IC50 in the nanomolar range against five Acanthamoeba isolates after 24 h and 96 h incubation. Confocal microscopy of trophozoites labelled with fluorescent S-MGB 363 (analogue of S-MGB235) showed this compound in the nucleus, nucleolus and distributed over the granuloplasm causing cell lysis, supporting the potent effect observed in vitro by S-MGB 235. Furthermore, conditions were standardised to establish Galleria mellonella larvae as a new in vivo infection model for A. castellanii Neff infections to assess the efficacy and toxicity of voriconazole, miltefosine and S-MGB 235. Voriconazole and miltefosine did not protect larvae from trophozoite infection, however S-MGB 235 significantly protected larvae when compared with the negative control. It was attempted to establish a CRISPR-Cas9 system for gene editing in Acanthamoeba. The plasmids pBRFPT7NeoCas9 and pBRFPT7PhleoCas9 (containing genes for the red fluorescent protein, T7 RNA polymerase, Cas9 along with the neomycin and phleomycin resistance genes, respectively, were constructed and transfected into A. castellanii Neff trophozoites using Xfect. Expression of RFP was confirmed by fluorescence microscopy and fluorescence-activated cell sorting.Acanthamoeba spp. are causative agents of a painful and severe sight-threatening corneal infection that can lead to blindness known as Acanthamoeba keratitis and a subacute disease in the brain which is usually fatal known as granulomatous amoebic encephalitis. Over the last few years, there has been a notorious increase in the number of infections due to Acanthamoeba spp. Poor diagnosis, problems of side effects, toxicity of the current drug treatment and the lack of gene editing tools as potential future therapy contribute to a high mortality rate. Strathclyde Minor Groove Binders (S-MGBs), compounds that bind to the minor groove of the DNA that designed and synthesised at University of Strathclyde were evaluated as potential alternative inhibitors against Acanthamoeba infections. Through cell viability microplate alamarBlue assays 42 S-MGBs were screened from which S-MGB 235 showed the most potent inhibitory effect with IC50 in the nanomolar range against five Acanthamoeba isolates after 24 h and 96 h incubation. Confocal microscopy of trophozoites labelled with fluorescent S-MGB 363 (analogue of S-MGB235) showed this compound in the nucleus, nucleolus and distributed over the granuloplasm causing cell lysis, supporting the potent effect observed in vitro by S-MGB 235. Furthermore, conditions were standardised to establish Galleria mellonella larvae as a new in vivo infection model for A. castellanii Neff infections to assess the efficacy and toxicity of voriconazole, miltefosine and S-MGB 235. Voriconazole and miltefosine did not protect larvae from trophozoite infection, however S-MGB 235 significantly protected larvae when compared with the negative control. It was attempted to establish a CRISPR-Cas9 system for gene editing in Acanthamoeba. The plasmids pBRFPT7NeoCas9 and pBRFPT7PhleoCas9 (containing genes for the red fluorescent protein, T7 RNA polymerase, Cas9 along with the neomycin and phleomycin resistance genes, respectively, were constructed and transfected into A. castellanii Neff trophozoites using Xfect. Expression of RFP was confirmed by fluorescence microscopy and fluorescence-activated cell sorting

Choice Models in Marketing: Economic Assumptions, Challenges and Trends

Direct utility models of consumer choice are reviewed and developed for understanding consumer preferences. We begin with a review of statistical models of choice, posing a series of modeling challenges that are resolved by considering economic foundations based on con-strained utility maximization. Direct utility models differ from other choice models by directly modeling the consumer utility function used to derive the likelihood of the data through Kuhn-Tucker con-ditions. Recent advances in Bayesian estimation make the estimation of these models computationally feasible, offering advantages in model interpretation over models based on indirect utility, and descriptive models that tend to be highly parameterized. Future trends are dis-cussed in terms of the antecedents and enhancements of utility function specification.