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In this paper, insight is given in the techniques used to compute asymptotic expansions. In a broad fashion the technique is described. Most of the results apply to the paper "An expansion for the maximum likelihood estimator and its…

We characterize the existence of the maximum likelihood estimator for discrete exponential families. Our criterion is simple to apply as we show in various settings, most notably for exponential models of random graphs. As an application,…

Distributions following a power-law are an ubiquitous phenomenon. Methods for determining the exponent of a power-law tail by graphical means are often used in practice but are intrinsically unreliable. Maximum likelihood estimators for the…

We derive an extended empirical likelihood for parameters defined by estimating equations which generalizes the original empirical likelihood for such parameters to the full parameter space. Under mild conditions, the extended empirical…

In decision-making, maxitive functions are used for worst-case and best-case evaluations. Maxitivity gives rise to a rich structure that is well-studied in the context of the pointwise order. In this article, we investigate maxitivity with…

Recently Balakrishnan and Iliopoulos [Ann. Inst. Statist. Math. 61 (2009)] gave sufficient conditions under which maximum likelihood estimator (MLE) is stochastically increasing. In this paper we study test plans which are not considered…

Triangular distributions are a well-known class of distributions that are often used as elementary example of a probability model. In the past, enumeration and order statistic-based methods have been suggested for the maximum likelihood…

A number of writers have supposed that for the full specification of belief, higher order probabilities are required. Some have even supposed that there may be an unending sequence of higher order probabilities of probabilities of…

We propose and study properties of maximum likelihood estimators in the class of conditional transformation models. Based on a suitable explicit parameterisation of the unconditional or conditional transformation function, we establish a…

In this paper, we consider approximating expansions for the distribution of integer valued random variables, in circumstances in which convergence in law cannot be expected. The setting is one in which the simplest approximation to the…

This paper proposes a widely applicable method of approximate maximum-likelihood estimation for multivariate diffusion process from discretely sampled data. A closed-form asymptotic expansion for transition density is proposed and…

In [3], we have introduced a probability measure to study the power and exponential sums for a certain coding system. The distribution function of the probability measure gives explicit formulas for the power and exponential sums.…

In multivariate or spatial extremes, inference for max-stable processes observed at a large collection of locations is among the most challenging problems in computational statistics, and current approaches typically rely on less expensive…

Triangular distributions are a well-known class of distributions that are often used as an elementary example of a probability model. Maximum likelihood estimation of the mode parameter of the triangular distribution over the unit interval…

A high order expansion of the renewal function is provided under the assumption that the inter-renewal time distribution is light tailed with finite moment generating function g on a neighborhood of 0. This expansion relies on complex…

Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…

In the current paper, the estimation of the probability density function and the cumulative distribution function of the Topp-Leone distribution is considered. We derive the following estimators: maximum likelihood estimator, uniformly…

The three-parameter generalized extreme value distribution arises from classical univariate extreme value theory and is in common use for analyzing the far tail of observed phenomena. Curiously, important asymptotic properties of…

Max-stable distributions and processes are important models for extreme events and the assessment of tail risks. The full, multivariate likelihood of a parametric max-stable distribution is complicated and only recent advances enable its…

Maximum-entropy distributions are shown to appear in the probability calculus as approximations of a model by exchangeability or a model by sufficiency, the former model being preferable. The implications of this fact are discussed,…