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Ricerche di Matematica (18273491)72(2)pp. 1-36
In this paper, we propose a flexible growth model that constitutes a suitable generalization of the well-known Gompertz model. We perform an analysis of various features of interest, including a sensitivity analysis of the initial value and the three parameters of the model. We show that the considered model provides a good fit to some real datasets concerning the growth of the number of individuals infected during the COVID-19 outbreak, and software failure data. The goodness of fit is established on the ground of the ISRP metric and the d2 -distance. We also analyze two time-inhomogeneous stochastic processes, namely a birth-death process and a birth process, whose means are equal to the proposed growth curve. In the first case we obtain the probability of ultimate extinction, being 0 an absorbing endpoint. We also deal with a threshold crossing problem both for the proposed growth curve and the corresponding birth process. A simulation procedure for the latter process is also exploited. © 2020, The Author(s).
Methodology and Computing in Applied Probability (13875841)25(3)
Several extensions of the familiar Dirichlet process have been widely investigated to nonparametric Bayesian model fittings parallel with appealing subsequent studies on their particular properties. This paper presents an explicit form for the joint distribution of drawn samples from the beta two-parameter process using an extension of stick-breaking construction. In particular, we evaluate the joint distribution of a random sequence for a specific process case and compare it with the Blackwell-MacQueen process. We obtain moments of the beta two-parameter process and present a formula for the number of distinct values in the sample. We establish the precision ratio and explore its effect on this number. © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Medical Journal Of The Islamic Republic Of Iran (10161430)36(1)
Background: Reliance heavily on out-of-pocket (OOP) payments, including informal payments (IPs), has undesired effects on financial risk protection and access to care. While a significant share of total health expenditure is spent on outpatient services, there is scant evidence of the patient's amount paid informally in outpatient services. Such evidence is available for inpatient services, showing the high prevalence of informal payments, ranging from 14 to 48% in the whole hospital. This study aimed to investigate the extent of OOP and IPs for outpatient services in Iran. Methods: A secondary data analysis of the 2015 IR Iran's Utilization of Healthcare Services (IrUHS) survey was conducted. A sample of 11,782 individuals with basic health insurance who were visited at least once by a physician in two private and public health care centers was included in this analysis. The percentage of OOP was determined and compared with the defined copayment (30%). The frequency of IPs was determined regarding the number of individuals who paid more than the defined copayments. The Mann-Whitney test also investigated the relationships between OOP percentage and IPs frequency with demographic variables. Results: The share that insured patients in Iran pay for a general practitioner (GP) visit was 38% in public versus 61% in the private sector, while for a specialist practitioner visit, the figures were 80% and 96%, respectively, which is higher than defined copayment (30%). This share was significantly higher in females, urban areas, highly educated people, private service providers, and specialist visits. The frequency of IPs, who paid more than the defined copayments, was 73% for a GP in public versus 86% in the private sector, while for a specialist practitioner visit, these were 90% and 93%, respectively. Conclusion: Informal patient payments for outpatient services are prevalent in Iran. Hence, more interventions are required to eliminate or control the IPs in outpatient services, particularly in the private sector. In this regard, making a well-regulated market, reinforcing the referral system, and developing an equity-oriented essential health services package would be fundamental © Iran University of Medical Sciences
Journal Of The Iranian Statistical Society (17264057)21(2)pp. 111-132
Bayesian nonparametric inference is increasingly demanding in statistical modeling due to incorporating flexible prior processes in complex data analysis. This paper represents the Polya urn scheme for the generalized Dirichlet process (GDP). It utilizes the partition analysis to construct the joint distribution of a random sample from the GDP as a mixture prior distribution of countable components. Using permutation theory, we present the components’ weights in a computationally accessible manner to make the resulting joint prior equation applicable. The advantages of our findings include tractable algebraic operations that lead to closed-form equations. The paper recommends the Polya urn Gibbs sampler algorithm, derive full conditional posterior distributions, and as an illustration, implement the algorithm for fitting some popular statistical models in nonparametric Bayesian settings. © 2023, (Iranian Statistical Society). All Rights Reserved.
Iranian Journal of Science and Technology, Transaction A: Science (10286276)45(3)pp. 1005-1014
The macroscopic behavior of networks, when facing random removal of nodes or edges, can be described as an inverse percolation process in a random graph. To determine whether a network remains operational when its elements (nodes or edges) fail at random, a “network robustness” criterion is used as a probabilistic measure. In this paper, we used percolation theory to assess this criterion for a network subjected to random failures of its elements. We then mapped the random failures process of the network into an inverse percolation problem. After that, based on the threshold for which the connectivity disappears, we assessed network robustness. Also, to demonstrate our method, we studied the robustness of systems that can be modeled as general inhomogeneous random graphs as well as scale-free random graphs. © 2021, Shiraz University.
Statistics and Applications (24547395)19(1)pp. 443-451
In recent years there has been a vast amount of work to model the spread of rumour. Here we review some of these mathematical models and present some of the main results. © 2021, Society of Statistics, Computer and Applications. All rights reserved.
Journal of Applied Statistics (02664763)47(16)pp. 3030-3052
A particular concerns of researchers in statistical inference is bias in parameters estimation. Maximum likelihood estimators are often biased and for small sample size, the first order bias of them can be large and so it may influence the efficiency of the estimator. There are different methods for reduction of this bias. In this paper, we proposed a modified maximum likelihood estimator for the shape parameter of two popular skew distributions, namely skew-normal and skew-t, by offering a new method. We show that this estimator has lower asymptotic bias than the maximum likelihood estimator and is more efficient than those based on the existing methods. © 2020 Informa UK Limited, trading as Taylor & Francis Group.
Journal of the Iranian Statistical Society (17264057)19(1)pp. 69-83
In this paper, we study an (n-k + 1)-out-of-n system by adopting their components to be statistically independent though nonidentically distributed. By assuming that at least m components at a fixed time have failed while the system is still working, we obtain the mixture representation of survival function for a quantity called the conditional inactivity time of failed components in the system. Moreover, this quantity for (n-k + 1)-out-of-n system, in one sample with respect to k and m and in two samples, are stochastically compared. © 2020 Iranian Statistical Society.
Indian Journal of Pure and Applied Mathematics (00195588)51(4)pp. 1661-1671
We consider a model of the spread of rumour among sceptical individuals. Let X0, X1,… be a {0, 1}-valued Markov chain and ρ0, ρ1, … a sequence of i.i.d. ℕ valued random variables independent of the Markov chain. An individual located at site i ∈ ℕ*:= ℕ ∪ {0} spreads the rumour to the individuals located in the interval [i, i + ρi] provided (i) Xi = 1 and (ii) if s/he has received the rumour from at least two distinct sources j, k < i with Xj = Xk = 1. To start the process we place two individuals at locations −1 and −2, each of spread the rumour to a distance ρ−1 and ρ−2 respectively to the right of itself. Here ρ−1 and ρ−2 are i.i.d. copies of ρ0. This extends the work of Sajadi and Roy [7] who considered the case when X0, X1,… is a sequence of i.i.d. {0,1} valued random variables, i.e. the believers {i: Xi = 1} and the disbelievers {i: Xi = 0} are located in an i.i.d. fashion. Here we study the case when the the believers and the disbelievers are located in a Markovian fashion. © 2020, Indian National Science Academy.
Journal of Statistical Physics (00224715)174(4)pp. 935-952
Junior et al. (J Appl Probab 48:624–636, 2011) studied a model to understand the spread of a rumour. Their model consists of individuals situated at the integer points of the line N. An individual at the origin 0 starts a rumour and passes it to all individuals in the interval [0 , R] , where R is a non-negative random variable. An individual located at i in this interval receives the rumour and transmits it further among individuals in [i, i+ Ri] where R and Ri are i.i.d. random variables. The rumour spreads in this manner. An alternate model considers individuals seeking to find the rumour from individuals who have already heard it. For this s/he asks individuals to the left of her/him and lying in an interval of a random size. We study these two models, when the individuals are more sceptical and they transmit or accept the rumour only if they receive it from at least two different sources. In stochastic geometry the equivalent of this rumour process is the study of coverage of the space Nd by random sets. Our study here extends the study of coverage of space and considers the case when each vertex of Nd is covered by at least two distinct random sets. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.
Iranian Journal of Science and Technology, Transaction A: Science (10286276)42(4)pp. 2183-2187
In this paper, we study the rate of convergence of the connectivity threshold of random geometric graphs when the underlying distribution of the vertices has no density. We consider n i.i.d. skew generalized Cantor distributed points on [0, 1] and we study the connectivity threshold of a random geometric graph that is built on these points. We show that for this graph, the connectivity threshold converges almost surely to a constant, similar result as in case of symmetric generalized Cantor distributed. We also study the rate of the convergence of this threshold in terms of the L1 norm. © 2017, Shiraz University.
Annals of Applied Probability (10505164)25(2)pp. 663-674
In this work we consider a simple SIR infection spread model on a finite population of n agents represented by a finite graph G. Starting with a fixed set of initial infected vertices the infection spreads in discrete time steps, where each infected vertex tries to infect its neighbors with a fixed probability β ∈ (0, 1), independently of others. It is assumed that each infected vertex dies out after an unit time and the process continues till all infected vertices die out. This model was first studied by [Ann. Appl. Probab. 18 (2008) 359-378]. In this work we find a simple lower bound on the expected number of ever infected vertices using breath-first search algorithm and show that it asymptotically performs better for a fairly large class of graphs than the upper bounds obtained in [Ann. Appl. Probab. 18 (2008) 359-378]. As a by product we also derive the asymptotic value of the expected number of the ever infected vertices when the underlying graph is the random r-regular graph and β < 1/r-1. © Institute of Mathematical Statistics, 2015.
Journal of Applied Probability (00219002)51(1)pp. 106-117
In this work we consider the mean-field traveling salesman problem, where the intercity distances are taken to be independent and identically distributed with some distribution F. We consider the simplest approximation algorithm, namely, the nearest-neighbor algorithm, where the rule is to move to the nearest nonvisited city. We show that the limiting behavior of the total length of the nearest-neighbor tour depends on the scaling properties of the density of F at 0 and derive the limits for all possible cases of general F. © Applied Probability Trust 2014.
Statistics and Probability Letters (01677152)82(12)pp. 2103-2107
For the connectivity of random geometric graphs, where there is no density for the underlying distribution of the vertices, we consider n i.i.d. Cantor distributed points on [0, 1]. We show that for such a random geometric graph, the connectivity threshold, R n, converges almost surely to a constant 1-2φ where 0<φ<1/2, which for the standard Cantor distribution is 1/3. We also show that {norm of matrix}Rn-(1-2φ){norm of matrix}1~2C(φ)n-1/dφ where C(φ)>0 is a constant and d φ{colon equals}-log2/logφ is the Hausdorff dimension of the generalized Cantor set with parameter φ. © 2012 Elsevier B.V..
