Distribution and correlation of Sabellidites cambriensis (Annelida?) in the basal Cambrian on Baltica

Sabellidites cambriensis is a tubular non-mineralized metazoan that appears as compressed ribbon-shaped imprints with transverse wrinkling, thick walls and an even tube diameter of up to 3 mm. The distribution of Sabellidites is investigated in three Ediacaran–Cambrian sections on the Digermulen Peninsula in Arctic Norway, spanning the Manndrapselva Member of the Stáhpogieddi Formation and the lower member of the Breidvika Formation. Here, the Ediacaran–Cambrian boundary is located in the lower part of the upper parasequence (third cycle) of the Manndrapselva Member. Specimens of Sabellidites are rare but consistently present close to the lowest level of Treptichnus pedum and upsection, whereas the taxon is common and abundant in the lower part of the lower member of the Breidvika Formation, with an upper record at c. 55 m above the base. The range is comparable with that of the GSSP section in Newfoundland, Canada, establishing Sabellidites as an index fossil for the lowermost Cambrian. In the Manndrapselva Member, Sabellidites co-occurs with the acritarch Granomarginata, indicative of the lowermost Cambrian Granomarginata Zone, whereas in the Breidvika Formation it co-occurs with Asteridium. Sabellidites is widely distributed in Baltica, through the Rovnian and Lontovan regional stages but confined to the Fortunian global stage. In its lower range, Sabellidites is associated with a Treptichnus pedum trace fossil association and a depauperate leiosphaerid acritarch assemblage, followed by a Granomarginata assemblage. In its upper range, Sabellidites co-occurs with acritarchs of the Asteridium–Comasphaeridium Zone and the tubular foraminiferan Platysolenites. In Baltica, Sabellidites is a useful index fossil.

The Moment Properties of Order, Reversed Order and Upper Record Statistics for the Power Ailamujia Distribution

The power Ailamujia distribution has been successfully developed in statistics, both theoretically and practically, performing well in the fitting of various types of data. This paper investigates the moment properties of the associated order, reversed order and upper record statistics, which are indeed unexplored aspects of this distribution. In particular, the exact expressions for the single moments of the order and reversed order statistics are provided. Some recurrence relationships for both single and product moments for the order and upper record statistics are proved. For additional goals, certain joint distributions are also given.

Simultaneous Joint Lower and Upper record values Probability Laws for Absolutely Continuous or Discrete Data

This paper investigates the probability density function (pdf) of the \((2n-1)\)-vector \((n\geq 1)\) of both lower and upper record values for a sequence of independent random variables with common \textit{pdf} \(f\) defined on the same probability space, provided that the lower and upper record times are finite up to \(n\). A lot is known about the lower or the upper record values when they are studied separately. When put together, the challenges are far complicated. The rare results in the literature still present some flaws. This paper begins a new and complete investigation with a few number of records: (n=2\) and \(n=3\). Lessons from these simple cases will allow addressing the general formulation of simultaneous joint lower-upper records.

Bayesian Estimations under the Weighted LINEX Loss Function Based on Upper Record Values

The essential objective of this research is to develop a linear exponential (LINEX) loss function to estimate the parameters and reliability function of the Weibull distribution (WD) based on upper record values when both shape and scale parameters are unknown. We perform this by merging a weight into LINEX to produce a new loss function called the weighted linear exponential (WLINEX) loss function. Then, we utilized WLINEX to derive the parameters and reliability function of the WD. Next, we compared the performance of the proposed method (WLINEX) in this work with Bayesian estimation using the LINEX loss function, Bayesian estimation using the squared-error (SEL) loss function, and maximum likelihood estimation (MLE). The evaluation depended on the difference between the estimated parameters and the parameters of completed data. The results revealed that the proposed method is the best for estimating parameters and has good performance for estimating reliability.

Characterization of a New Family of Distribution Through Upper Record Values

In this paper, a new class of distribution has been characterized through the condi- tional expectations, conditioned on a non-adjacent upper record value. Also an equivalence between the unconditional and conditional expectation is used to characterize the new class of distribution.

Kumaraswamy inverse Gompertz distribution: Properties and engineering applications to complete, type-II right censored and upper record data

This article proposes and studies a new three-parameter generalized model of the inverse Gompertz distribution, in the so-called Kumaraswamy inverse Gompertz distribution. The main advantage of the new model is that it has "an upside down bathtub-shaped curve hazard rate function" depending upon the shape parameters. Several of its statistical and mathematical properties including quantiles, median, mode, moments, probability weighted moment, entropy function, skewness and kurtosis are derived. Moreover, the reliability and hazard rate functions, mean time to failure, mean residual and inactive lifetimes are also concluded. The maximum likelihood approach is done here to estimate the new model parameters. A simulation study is conducted to examine the performance of the estimators of this model. Finally, the usefulness of the proposed distribution is illustrated with different engineering applications to complete, type-II right censored, and upper record data and it is found that this model is more flexible when it is compared to well-known models in the statistical literature.