A new species of the genus Fredius Pretzmann, 1967 (Decapoda: Brachyura: Pseudothelphusidae) from Brazil, with comments on the southerly distribution of the family

A new species of pseudothelphusid crab of the tribe Kingsleyini Ortmann, 1897, from the southern Amazon region in the state of Rondônia, Brazil, is described and illustrated. Fredius avilai n. sp. can be readily distinguished from its congeners by the following characters of the male first gonopod: mesial lobe elongated, convoluted, proximal portion directed laterally, distal portion sharply recurved in abdominal direction; marginal process rounded, not projected over distal opening of spermatic channel, merging with distal portion of abdominal surface after a shallow depression; lateral suture well demarcated along mesoabdominal surface of stem, distal portion directed inwards. The assignment of the new species to the genus Fredius Pretzmann, 1967 and its affinities with another closed related species are discussed.

Explicit Formula for Average Run Length of Double Moving Control Chart for INAR(1) Processes

Count data are used in many fields of practice, especially Poisson distribution as a popular choice for the marginal process distribution. If these counts exhibit serial dependence, a popular approach is to use a Poisson INAR(1) model to describe the autocorrelation structure of process. In this paper, the explicit formulas are proposed to evaluate performance characteristics of Double Moving Average control chart (DMA) for Integer valued autoregressive of serial dependence Poisson process. The characteristics of the control chart are frequently measured as Average Run Length (ARL) which means that the average of observations are taken before a system is signaled to be out-of-control. These proposed explicit formulas of ARL are simple and easy to implement for practitioner. The numerical results show that the DMA chart performs better than others when the magnitudes of shift are moderate and large.

On a class of multivariate counting processes

In this paper we define and study a new class of multivariate counting processes, named `multivariate generalized Pólya process'. Initially, we define and study the bivariate generalized Pólya process and briefly discuss its reliability application. In order to derive the main properties of the process, we suggest some key properties and an important characterization of the process. Due to these properties and the characterization, the main properties of the bivariate generalized Pólya process are obtained efficiently. The marginal processes of the multivariate generalized Pólya process are shown to be the univariate generalized Pólya processes studied in Cha (2014). Given the history of a marginal process, the conditional property of the other process is also discussed. The bivariate generalized Pólya process is extended to the multivariate case. We define a new dependence concept for multivariate point processes and, based on it, we analyze the dependence structure of the multivariate generalized Pólya process.

A new species of freshwater crab of the genus Allacanthos Smalley, 1964 (Crustacea, Decapoda, Pseudothelphusidae) from southern Costa Rica, Central America

A new species of pseudothelphusid crab, Allacanthos yawi n. sp., from the Río Volcán drainage, Puntarenas Province, southern Costa Rica, Central America, is described and illustrated. This is the second species to be assigned to the genus Allacanthos Smalley, 1964. The new species is distinguished by its congener by having a first gonopod with a mesiolaterally flattened distal portion, a concave and nearly smooth subdistal portion of the lateral and cephalic sides, a narrow marginal process with a nearly straight distal border, and a lateral lobe with a sharp tip on the apex. An amended diagnosis for Allacanthos is provided.

Analysis of a counting process associated with a semi-Markov process: number of entries into a subset of state space

Let N(t) be a finite semi-Markov process on 𝒩 and let X(t) be the associated age process. Of interest is the counting process M(t) for transitions of the semi-Markov process from a subset G of 𝒩 to another subset B where 𝒩 = B ∪ G and B ∩ G = ∅. By studying the trivariate process Y(t) =[N(t), M(t), X(t)] in its state space, new transform results are derived. By taking M(t) as a marginal process of Y(t), the Laplace transform generating function of M(t) is then obtained. Furthermore, this result is recaptured in the context of first-passage times of the semi-Markov process, providing a simple probabilistic interpretation. The asymptotic behavior of the moments of M(t) as t → ∞ is also discussed. In particular, an asymptotic expansion for E[M(t)] and the limit for Var [M(t)]/t as t → ∞ are given explicitly.

Analysis of a counting process associated with a semi-Markov process: number of entries into a subset of state space

Let N(t) be a finite semi-Markov process on 𝒩 and let X(t) be the associated age process. Of interest is the counting process M(t) for transitions of the semi-Markov process from a subset G of 𝒩 to another subset B where 𝒩 = B ∪ G and B ∩ G = ∅. By studying the trivariate process Y(t) =[N(t), M(t), X(t)] in its state space, new transform results are derived. By taking M(t) as a marginal process of Y(t), the Laplace transform generating function of M(t) is then obtained. Furthermore, this result is recaptured in the context of first-passage times of the semi-Markov process, providing a simple probabilistic interpretation. The asymptotic behavior of the moments of M(t) as t → ∞ is also discussed. In particular, an asymptotic expansion for E[M(t)] and the limit for Var [M(t)]/t as t → ∞ are given explicitly.

Calculating extinction probabilities for the birth and death chain in a random environment

In a previous investigation (Torrez (1978)) conditions were given for extinction and instability of a stochastic process (Zn ) evolving in a random environment controlled by an irreducible Markov chain (Yn ) with state space 𝒴 The process (Yn, Zn ) is Markovian with state space 𝒴 × {0,1, ···, N} where 𝒴 = {1,· ··,m} and the marginal process (Zn ) is a birth and death chain on {0,1,· ··,N}, with 0 and N made absorbing, when conditioned on a fixed sequence of environmental states of (Yn ). This paper provides bivariate finite difference methods for calculating (i) P(Zn → 0) when this probability is not one; and (ii) the expected duration of the process Zn. For (i), the cases when the transition probabilities of the (Yn )-conditioned process (Zn ) are non-homogeneous and homogeneous are considered separately. Examples are given to illustrate these methods.