The lognormal moment sequence is considered. Using the fractional moments technique, it is first proved that the lognormal has the largest differential entropy among the infinite positively supported probability densities with the same lognormal-mome...
The Shewhart X¯- and S-charts are most commonly used for monitoring the process mean and variability based on the assumption of normality. However, many process distributions may follow a positively skewed distribution, such as the lognormal distribu...
Instantaneous volatility of logarithmic return in the lognormal fractional SABR model is driven by the exponentiation of a correlated fractional Brownian motion. Due to the mixed nature of driving Brownian and fractional Brownian motions, probability...
Control charts, one of the powerful tools in statistical process control (SPC), are widely used to monitor and detect out-of-control processes in the manufacturing industry. Many researchers have pointed out the effects of using estimated parameters...
In this paper, the lognormal distribution is studied, and a new series representation is proposed. This series uses the powers of the bilinear function. From it, a simplified form is obtained and used to compute the Laplace transform of the distribut...
In this paper, we perform the computation of the Laplace-Stieljes transform of Lognormal and Weibull distribution, in which the upper limit of the definite integral from infinite to 1 by using proper transformation. Some advantages are found in this...
As a result of asymmetry in practical problems, the Lognormal distribution is more suitable for data modeling in biological and economic fields than the normal distribution, while biases of maximum likelihood estimators are regular of the order O...
In the short time to maturity limit, it is proved that for the conditionally lognormal SABR model the zero vanna implied volatility is a lower bound for the volatility swap strike. The result is valid for all values of the correlation parameter and i...
The paper presents a phenomenological epidemiological model for the description and prediction of the time trends of COVID-19 deaths worldwide. A bimodal distribution function—defined as the mixture of two lognormal distributions—is assum...
In recent years, the Poisson lognormal mixed model has been frequently used in modeling count data because it can accommodate both the over-dispersion of the data and the existence of within-subject correlation. Since the likelihood function of this...
A delta-lognormal distribution consists of zero and positive values. The positive values follow a lognormal distribution, which is an asymmetric distribution. It is well known that the logarithm of these values follows a normal distribution, which is...
Different versions of the lognormal diffusion process with exogenous factors have been used in recent years to model and study the behavior of phenomena following a given growth curve. In each case considered, the estimation of the model has been add...
Influence analysis is a critical diagnostic tool in regression modeling to ensure reliable parameter estimates. This study evaluates the effectiveness of diagnostic methods for detecting influential observations in the lognormal regression model usin...
The log-normal distribution (skewed distribution or asymmetry distribution) is used to describe random variables comprising positive real values. It is well known that the logarithm values of these are normally distributed (symmetry distribution). Po...
The length-biased lognormal distribution is a length-biased version of lognormal distribution, which is developed to model the length-biased lifetime data from, for example, biological investigation, medical research, and engineering fields. Owing to...
The coefficient of quartile variation is a valuable measure used to assess data dispersion when it deviates from a normal distribution or displays skewness. In this study, we focus specifically on the delta-lognormal distribution. The lognormal distr...
Probabilistic models with flexible tail behavior have important applications in engineering and earth science. We introduce a nonlinear normalizing transformation and its inverse based on the deformed lognormal and exponential functions proposed by K...
Generalized linear models might not be appropriate when the probability of extreme events is higher than that implied by the normal distribution. Extending the method for estimating the parameters of a double Pareto lognormal distribution (DPLN) in R...
There are various distributions of image histograms where regions form symmetrically or asymmetrically based on the frequency of the intensity levels inside the image. In pure image processing, the process of optimal thresholding tends to accurately...
Background subtraction is a core preprocessing step for video analytics, enabling downstream tasks such as detection, tracking, and scene understanding in applications ranging from surveillance to transportation. However, real-time deployment remains...
In this paper, we study a new family of Gompertz processes, defined by the power of the homogeneous Gompertz diffusion process, which we term the powers of the stochastic Gompertz diffusion process. First, we show that this homogenous Gompertz diffus...
Switched-mode power supplies (SMPSs) are an important component in many electrical systems. As a highly non-linear device, an unavoidable side-effect of SMPS operation is its high harmonics power. One of the ways to model the harmonic power consumpti...
Collaborative robots or cobots interact with humans in a common work environment. In cobots, one under-investigated but important issue is related to their movement and how it is perceived by humans. This paper tries to analyze whether humans prefer...
In this work, the nearest-neighbor distances and Voronoi cell features of Cu-Ag deposits were analyzed and fitted with Lognormal, Weibull, and Gamma distributions. The nearest-neighbor distance distributions of the samples were compared with those of...
To solve the timing uncertainty in low-voltage circuits, this paper proposes an analytical sequential path delay model based on the lognormal distribution. Unlike previous works that primarily focus on combinational logic, our model provides a comple...
This paper presents a comparative study of classical and Bayesian risks in the design of optimal failure-censored sampling plans for lognormal lifetime models. The analysis focuses on how variations in prior distributions, specifically the beta distr...
Performance evaluation tools for wireless cellular systems are very important for the establishment and testing of future internet applications. As the complexity of wireless networks keeps growing, wireless connectivity becomes the most critical req...
We study spatial scaling and complexity properties of Amazonian radar rainfall fields using the Beta-Lognormal Model (BL-Model) with the aim to characterize and model the process at a broad range of spatial scales. The Generalized Space q-Entropy Fun...
With the difference in the photosynthesis process between C3- and C4-plants, the 13C/12C stable isotope ratio of ethanol, i.e., δ13C-ethanol, can potentially be a basis for the discrimination of Scotch whiskies derived from different raw materi...
This study evaluates the effect of considering data intermittency and log-normality in applications of simple Kriging. Several sets of synthetic data, both intermittent and log-normal, were prepared for this purpose, and then four different Kriging a...
We introduce a quantile-based multivariate log-normal distribution, providing a new multivariate skewed distribution with positive support. The parameters of this distribution are interpretable in terms of quantiles of marginal distributions and asso...
It is typically difficult to estimate the number of degrees of freedom due to the leptokurtic nature of the Student t-distribution. Particularly in studies with small sample sizes, special care is needed concerning prior choice in order to ensure tha...
Blazars are highly variable and display complex characteristics. A key characteristic is the flux probability distribution function or flux PDF whose shape depends upon the form of the underlying physical process driving variability. The BL Lacertae...
In this article, we propose approaches for constructing confidence intervals for the single signal-to-noise ratio (SNR) of a log-normal distribution and the difference in the SNRs of two log-normal distributions. The performances of all of the approa...
We analytically derived and confirmed by empirical data the following three relations from the quasi-time-reversal symmetry, Gibrat’s law, and the non-Gibrat’s property observed in the urban population data of France. The first is the relation betwee...
In this work, we approach the forecast problem for a general non-homogeneous diffusion process over time with a different perspective from the classical one. We study the main characteristic functions as mean, mode, and α-quantiles conditioned...
Despite the widespread use of chain-ladder models, so far no theory was available to test for model specification. The popular over-dispersed Poisson model assumes that the over-dispersion is common across the data. A further assumption is that accid...
This paper examines different distribution functions used in a three-moment parameterization scheme with regard to their influence on the implementation and the results of the parameterization scheme. In parameterizations with moment methods, the pro...
In this paper, we study the inferences of the difference of medians for two independent log-normal distributions. These methods include traditional methods such as the parametric bootstrap approach, the normal approximation approach, the method of va...
The power of projection using divergence functions is a major theme in information geometry. One version of this is the variational Bayes (VB) method. This paper looks at VB in the context of other projection-based methods in information geometry. It...
In this survey, a short introduction of the recent discovery of log-normally-distributed market-technical trend data will be given. The results of the statistical evaluation of typical market-technical trend variables will be presented. It will be sh...
The mechanosensitivity of cells has recently been identified as a process that could greatly influence a cell’s fate. To understand the interaction between cells and their surrounding extracellular matrix, the characterization of the mechanical...
Many studies have underlined the importance of the log-normal distribution in the modeling of phenomena occurring in biology. With this in mind, in this article we offer a new and motivated transformed version of the log-normal distribution, primaril...
This paper develops Bayesian inference in reliability of a class of scale mixtures of log-normal failure time (SMLNFT) models with stochastic (or uncertain) constraint in their reliability measures. The class is comprehensive and includes existing fa...
A bimodal double log-normal distribution on the real line is proposed using the random sign mixture transform. Its associated statistical inferences are derived. Its parameters are estimated by the maximum likelihood method. The performance of the es...
The determination of the luminosity function (LF) in Gamma ray bursts (GRBs) depends on the adopted cosmology, each one characterized by its corresponding luminosity distance. Here, we analyze three cosmologies: the standard cosmology, the plasma cos...
Using the classical received signal strength (RSS)-distance log-normal model in wireless sensor network (WSN) applications poses a series of characteristic challenges derived from (a) the model’s structural limitations when it comes to explaining rea...
This paper addresses polarimetric adaptive coherent detection of radar targets embedded in sea clutter. Initially, radar clutter data across multiple polarimetric channels is modeled using a compound Gaussian framework featuring an unspecified speckl...
This paper discusses inferential approaches for the problem of constant-stress accelerated life testing when the failure data are progressive type-I interval censored. Both frequentist and Bayesian estimations are carried out under the assumption tha...
27 March 2014
We compared six methods for regression on log-normal heteroscedastic data with respect to the estimated associations with explanatory factors (bias and standard error) and the estimated expected outcome (bias and confidence interval). Method comparis...
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