Parameter Estimation Research Articles

Influences of service, reference groups and framing effects on the intentions of short-term rental users

ABSTRACT This study examines the influences of short-term rental services, reference groups, and information framing effects on consumers’ intentions to rent short-term rental properties. This study used a behavioural economics approach to analyze consumers’ intentions towards renting short-term rental properties. Using the concepts of reference groups and framing effects in addition to the three factors of location, price, and short-term rental services, this study proposes a conceptual framework model. Structural equation modelling was used for the parameter estimation. The study area included Kaohsiung City and Pingtung County. A total of 314 questionnaires were administered, from which 305 valid responses were obtained, indicating an effective response rate of 97.10%. The empirical results reveal that short-term rental services, reference groups, and framing effects had no direct significant influences on rental intentions. However, the three variables had indirect influences on rental intentions through the full mediator variable of attitudes. These findings highlight the importance of rental services, reference groups, and framing effects in analyzing consumers’ intentions towards short-term rental services.

Estimation of PEMFC optimal parameters based on an improved butterfly optimization algorithm.

This paper introduces a novel butterfly optimization algorithm, called the spiral search and dynamic crossover based butterfly optimization algorithm (SCBO), for parameter estimation in proton exchange membrane fuel cell (PEMFC) models. To enhance the global performance of the butterfly algorithm, a spin-search strategy is incorporated to expand its exploration range, while an adaptive factor is introduced to strike a balance between exploration and exploitation. Additionally, a dynamic crossover operation is integrated to enhance solution diversity, addressing the algorithm's tendency to converge to local optima. Extensive experimentation on benchmark functions in comparison with common optimization algorithms demonstrates that SCBO outperforms others in terms of convergence accuracy and speed. Finally, we employ SCBO for parameter identification in a PEMFC model, showcasing its superior results and its ability to capture the model's dynamics when compared to other algorithms.

Measuring associations between the food environment and dietary habits: comparing the proportion and density of food outlets

BackgroundThe food environment plays a crucial role in shaping our dietary choices and overall health. Spatial measures provide distinct perspectives on the physical food environment and its impact on diet. While proportion measures are theoretically considered to provide a more accurate representation of the overall physical food environment than density measures, it is important to recognize that the association between food environments and diet can vary depending on the context. Therefore, relying solely on one measure may not be appropriate.MethodsWe systematically assessed the density and proportion of multiple food outlet types (fast-food outlets, convenience stores, supermarkets, and restaurants) around individuals homes using a large cross-sectional Danish study (N = 71,840). Densities were modeled in separate multilevel linear regression models, incorporating random intercepts from linear splines for each of the four food outlet types. Proportions were modeled without splines. Through the association with a dietary quality score (DQS), we examined the impact of quantifying the foodscape from density versus proportion measures. Associations were compared using parameter estimates, p-values, Akaike Information Criterion (AIC) values, and Akaike weights.ResultsAIC values and Akaike weights were in favor of models including density measures. Across all outlet types, density measures were consistently negatively associated with the DQS until reaching densities of 3–5 (count/km2), at which point the direction of association became positive, indicating a shift towards a healthier DQS. After correcting for multiple comparisons, the most significant effect was observed for the sole significant proportion measure. A 10% increase in the proportion of fast-food outlets among "eating out options" was associated with a 7% decrease in the DQS, towards poorer dietary quality.ConclusionsThe associations highlight that choosing food outlet density versus proportions to quantify the foodscape impact findings of substantial importance when considering the significance level and direction of association. Findings suggests a threshold effect when using density measures indicating abundance of many food outlets, at which the association with dietary quality alters significantly towards healthier diet quality.

Evaluation of WIMU Sensor Performance in Estimating Running Stride and Vertical Stiffness in Football Training Sessions: A Comparison with Smart Insoles

Temporal parameters are crucial for understanding running performance, especially in elite sports environments. Traditional measurement methods are often labor-intensive and not suitable for field conditions. This study seeks to provide greater clarity in parameter estimation using a single device by comparing it to the gold standard. Specifically, this study aims to investigate how the temporal parameters and vertical stiffness (Kvert) of running stride exerted by IMU sensors are related to the parameters of the smart insole for outdoor acquisition. Ten healthy male subjects performed four 60-meter high-speed runs. Data were collected using the WIMU PRO™ device and smart insoles. Contact time (CT) and flight time (FT) were identified, and Kvert was calculated using Morin’s method. Statistical analyses assessed data normality, correlations, and reliability. WIMU measured longer CT, with differences ranging from 26.3% to 38.5%, and shorter FT, with differences ranging from 27.3% to 54.5%, compared to smart insoles, across different running speeds. Kvert values were lower with WIMU, with differences ranging from 23.96% to 45.01% depending on the running activity, indicating significant differences (p < 0.001). Using these results, a multiple linear regression model was developed for the correction of WIMU’s Kvert values, improving the accuracy. The improved accuracy of Kvert measurements has significant implications for athletic performance. It provides sports scientists with a more reliable metric to estimate player fatigue, potentially leading to more effective training regimens and injury prevention strategies. This advancement is particularly valuable in team sports settings, where easy-to-use and accurate biomechanical assessments of multiple athletes are essential.

Stellar atmospheric parameters and chemical abundances of ~ 5 million stars from S-PLUS multiband photometry

The APOGEE, GALAH, and LAMOST spectroscopic surveys have substantially contributed to our understanding of the Milky Way by providing a wide range of stellar parameters and chemical abundances. Complementing these efforts, photometric surveys that include narrowband and medium-band filters, such as Southern Photometric Local Universe Survey (S-PLUS), provide a unique opportunity to estimate the atmospheric parameters and elemental abundances for a much larger number of sources, compared to spectroscopic surveys. Our aim is to establish methodologies for extracting stellar atmospheric parameters and selected chemical abundances from S-PLUS photometric data, which cover approximately $3000$ square degrees, by applying seven narrowband and five broadband filters. We used all 66 S-PLUS colors to estimate parameters based on three different training samples from the LAMOST, APOGEE, and GALAH surveys, applying cost-sensitive neural network (NN) and random forest (RF) algorithms. We kept the stellar abundances that lacked corresponding absorption features in the S-PLUS filters to test for spurious correlations in our method. Furthermore, we evaluated the effectiveness of the NN and RF algorithms by using estimated $T_ eff $ and \( g\) values as the input features to determine other stellar parameters and abundances. The NN approach consistently outperforms the RF technique on all parameters tested. Moreover, incorporating $T_ eff $ and \( g\) leads to an improvement in the estimation accuracy by approximately $3<!PCT!>$. We kept only parameters with a goodness-of-fit higher than $50<!PCT!>$. Our methodology allowed us to obtain reliable estimates for fundamental stellar parameters ($T_ eff g\), and Fe/H ) and elemental abundance ratios such as alpha /Fe Al/Fe C/Fe Li/Fe and Mg/Fe for approximately five million stars across the Milky Way, with a goodness-of-fit above $60<!PCT!>$. We also obtained additional abundance ratios, including Cu/Fe O/Fe and Si/Fe . However, these ratios should be used cautiously due to their low accuracy or lack of a clear relationship with the S-PLUS filters. Validation of our estimations and methods was performed using star clusters, Transiting Exoplanet Survey Satellite (TESS) data and Javalambre Photometric Local Universe Survey (J-PLUS) photometry, further demonstrating the robustness and accuracy of our approach. By leveraging S-PLUS photometric data and advanced machine learning techniques, we have established a robust framework for extracting fundamental stellar parameters and chemical abundances from medium-band and narrowband photometric observations. This approach offers a cost-effective alternative to high-resolution spectroscopy. The estimated parameters hold significant potential for future studies, particularly when classifying objects within our Milky Way or gaining insights into its various stellar populations.

Regularized Variational Approximation for Partially Confirmatory Factor Analysis

The recently developed partially confirmatory factor analysis (PCFA) framework offers a promising solution that effectively accommodates varying levels of available knowledge, blending the strengths of both data- and theory-driven approaches. Nevertheless, its reliance on Markov Chain Monte Carlo (MCMC) techniques for parameter estimation often comes with challenges due to its computationally intensive nature and issues related to convergence. To address that, this study introduces a novel and compelling alternative - the regularized variational approximation approach within the PCFA framework (PCFA-VA). The proposed method integrates regularization techniques and converts the classical Bayesian inference problem into an optimization problem by approximating the posterior distribution with a predefined family of distributions and employing Kullback–Leibler (KL) divergence to quantify such differences. In this sense, PCFA-VA avoids the complex integration problem required to obtain the exact posterior distribution and results in substantial computational savings. Based on the simulated and real data analysis, PCFA-VA has demonstrated the potential to achieve considerable accuracy while maintaining computational efficiency, making it scalable for large-scale problems.

Population Pharmacokinetic Modeling to Support Trofinetide Dosing for the Treatment of Rett Syndrome.

Oral trofinetide administered using a body weight-banded dosing regimen was approved in the US for the treatment of Rett syndrome (RTT) in patients aged≥2years. This approval was principally based on efficacy and safety findings of the phase 3 LAVENDER study in girls and women aged 5-20years with RTT and extended to younger children aged 2-4years with supporting data from the DAFFODIL study. Weight-banded dosing regimens were selected based on early clinical population pharmacokinetic (popPK) modeling and different scenario simulations. We report the development and application of an updated popPK model to confirm that steady-state trofinetide exposures achieved in individual patients in the LAVENDER study were within target exposure range. A previously developed popPK model using data from nine clinical studies was updated based on 13 clinical studies of trofinetide in healthy volunteers and pediatric and adult patients, including the LAVENDER study. PopPK model and empiric individual Bayesian pharmacokinetic parameter estimates were used to generate trofinetide exposures. Covariate data from the pharmacokinetic dataset from LAVENDER study subjects (n=92) were used to estimate individual steady-state trofinetide exposure (area under concentration-time curve over 0-12 h [AUC0-12]). Steady-state exposures in individual patients in the LAVENDER study were used to confirm that the dosing regimens resulted in exposures within the target range. Among 5- to 20-year-olds receiving the LAVENDER BID dosing regimen [trofinetide 6g(12‒20kg), 8g(>20‒35kg), 10g(>35‒50kg), and 12g(>50kg)], simulated AUC0-12 values overlapped with the target exposure range; median AUC0-12 values were within target exposure range for all weight bands. PopPK model-based simulations confirm that weight-banded trofinetide dosing used in LAVENDER in girls and women aged 5-20years with RTT achieved target exposure. Graphical abstract available for this article.

Population Pharmacokinetics of Trofinetide in a Pediatric Population Aged 2-4Years with Rett Syndrome.

Weight-banded trofinetide dosing improved physician- and caregiver-rated efficacy measures and had acceptable tolerability in patients aged 2‒4years (DAFFODIL study) and 5‒20years (LAVENDER study) with Rett syndrome (RTT). Selection of weight-banded dosing regimens for these studies was based on population pharmacokinetic (popPK) modeling and exposure simulations. This study applied an updated popPK model to confirm steady-state trofinetide exposures achieved in DAFFODIL patients were within target range. A popPK model was developed using data from 14 clinical studies of trofinetide in healthy volunteers and pediatric and adult patients, including the LAVENDER and DAFFODIL studies. Individual exposure measures (area under concentration-time curve over 0-12h [AUC0-12] were generated via integration of the predicted concentration-time profile for each DAFFODIL study participant based on the popPK model and individual empiric Bayesian pharmacokinetic parameter estimates. Distributions of steady-state AUC0-12 values for each body-weight group were compared against target exposure (AUC0-12 = 800‒1200µg·h/mL). Distribution and box plots of simulated steady-state AUC0-12 values achieved with the weight-banded DAFFODIL dosing regimen used in younger individuals aged 2-4years with RTT (twice daily trofinetide 5g[≥ 9 to < 12kg] or 6g [≥ 12 to < 20kg]) indicated good overlap with the target exposure range. Median steady-state AUC0-12 values for both body-weight bands fell within the target exposure range. PopPK model-based simulations confirm that the weight-banded dosing regimen used in DAFFODIL is adequate to achieve target trofinetide exposure in 2- to 4-year-olds with RTT.

Adaptive compensation for multi-axial real-time hybrid simulation via nonlinear parameter estimation

For Real-time hybrid simulation (RTHS) to be stable and accurate, it is essential to address the time desynchronization issue between the numerical and physical substructures. Desynchronization is primarily caused by time delays, inherent dynamics of the control plant, system uncertainties, and noises. While existing adaptive compensators have shown effective tracking performance in single-input single-output (SISO) RTHS, their effectiveness in multi-input multi-output (MIMO) RTHS has not been fully demonstrated. MIMO-RTHS presents additional challenges due to its larger solution space, and significant dynamic coupling between actuators. To address these challenges, this study introduces an adaptive compensation framework for MIMO-RTHS. The proposed framework utilizes a control law based on the inverse dynamics of the control plant, incorporating real-time adaptive parameter updates through Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) methods. Both the transfer function (TF) and discrete-time state-space (SS) models of the plant are employed in distinct parameter estimation cases. The performance of the proposed compensation is validated through a multi-axial RTHS (maRTHS) benchmark problem. Extensive simulations on the maRTHS incorporating various earthquake inputs, sensor noise, and model uncertainties, demonstrated an excellent tracking performance and strong robustness across four parameter estimation cases (EKF-TF, UKF-TF, EKF-SS, and UKF-SS). The use of UKF with SS model (UKF-SS) achieved superior performance, effectively managing nonlinearities and noise without requiring low-pass filtering.

Gwforge: a user-friendly package to generate gravitational-wave mock data

Abstract Next-generation gravitational-wave detectors, with their improved sensitivity and wider frequency bandwidth, will be capable of observing almost every compact binary coalescence signal from epochs before the first stars began to form, increasing the number of detectable binaries to hundreds of thousands annually. This will enable us to observe compact objects through cosmic time, probe extreme matter phenomena, do precision cosmology, study gravity in strong field dynamical regimes and potentially allow observation of fundamental physics beyond the standard model. However, the richer data sets produced by these detectors will pose new computational, physical and astrophysical challenges, necessitating the development of novel algorithms and data analysis strategies. To aid in these efforts, this paper introduces gwforge, a user-friendly, lightweight Python package, to generate mock data for next-generation detectors. gwforge allows users to seamlessly simulate data while abstracting away technical complexities, enabling more efficient testing and development of analysis pipelines. Additionally, the package’s data generation process is optimized using high-throughput systems like HTCondor, significantly speeding up the simulation of large populations of gravitational-wave events. We demonstrate the package’s capabilities through data simulation examples and highlight a few potential applications: performance loss due to foreground noise, bright-siren cosmology and impact of waveform systematics on binary parameter estimation.

On the calibration of multiscale geographically and temporally weighted regression models

Spatiotemporal analysis and modeling have long been key foci of geographical information science. In a recent paper, Wu et al. expanded the local spatial modeling technique of multiscale geographically weighted regression (MGWR) to incorporate a temporal component. This new model is named multiscale geographically and temporally weighted regression (MGTWR). Despite the utility of expanding MGWR to incorporate a temporal weighting function in addition to the existing spatial one, the approach developed by Wu et al. has two limitations: the bandwidth selection algorithm cannot guarantee an optimal result and no formulation for the effective number of parameters (ENPs) in the model is given. To address these issues, this paper describes a procedure to derive an optimal temporal and an optimal spatial bandwidth for MGTWR and also develops a formula for the ENPs in the model. The former ensures the reliability of the model outputs while the latter is essential for making reliable inferences from the local parameter estimates generated in the calibration of models by MGTWR. These advances in the MGTWR framework are demonstrated through applications to simulated and real-world data.

An Evaluation of the Sensitivity of a Source Term Estimation Methodology of Sensor Configuration in an Urban-like Environment

Identifying unknown sources of air pollutants is vital for protecting public health, especially in cases involving the emission of toxic substances. The efficiency of this process depends highly on the accuracy of Source Term Estimation (STE) methods and the availability of robust measurements. Therefore, it is important to examine how sensor network characteristics affect STE accuracy. This study investigates the impact of different sensor configurations on STE results for a stationary point source in a complex, urban-like environment. The STE methodology employs the Metropolis–Hastings Markov Chain Monte Carlo (MCMC) algorithm alongside numerical simulations of a Computational Fluid Dynamics (CFD) model. The STE algorithm is applied across several sensor configurations in three distinct release scenarios and real sensor observations from the Michelstadt wind tunnel experiment, assessing both the number of sensors used and the agreement between measured and modeled concentrations. In general, the results indicate that increasing the number of sensors and the model’s accuracy improves the source parameters estimations. However, there is a specific number of sensors in each release scenario where STE outcomes from randomly selected, high-accuracy, and low-accuracy sensors converge to similar solutions. Overall, the findings provide valuable information for designing sensor configurations in urban areas.

SCEC/USGS Community Stress-Drop Validation Study: How Spectral Fitting Approaches Influence Measured Source Parameters

ABSTRACT Spectral source parameters used to estimate an earthquake’s stress drop (Δσ) can vary significantly across measurement approaches. The Statewide California Earthquake Center/U.S. Geological Survey Community Stress-Drop Validation Study was initiated to compare source parameter estimates, focusing initially on a dataset from the 2019 Ridgecrest earthquake sequence. As part of that validation effort, here we focus on one potential source of uncertainty: whether spectral fitting approaches alone, applied to a common set of spectra from the 2019 Ridgecrest sequence result in different source parameter estimates. By using a common set of benchmark spectra analyzed across a consistent frequency band of 1–40 Hz, we eliminate many sources of variability. A subgroup of validation study participants volunteered to estimate the low-frequency displacement (Ω0) and corner frequency (fc) by fitting a smooth function to benchmark displacement spectra. Participants used linear- or log-sampled spectra, assumed a Brune or Boatwright spectral model, and applied different misfit criteria. We compare 17 approaches used to estimate Ω0, fc, and Δσ for 54 earthquake spectra. Our results reveal that 35% of events have Δσ estimates within a factor of two, whereas others exhibit variations exceeding an order of magnitude. The variability in Ω0 and fc can largely be attributed to whether a spectrum is consistent with the smooth function of an idealized simple crack model. The trade-off between Ω0 and fc may be more pronounced when using linearly sampled spectra, as higher frequency spectral bumps control the fits. As expected, methods that assumed a Boatwright model tended to have lower Ω0 and somewhat higher fc compared to those assuming a Brune model, although resulting Δσ estimates are similar. When compared to the overall validation study results, the fitting approach alone may account for between 5% and 90% (25% on average) of the total variability in spectral Δσ.

Comparing AI versus Optimization Workflows for Simulation-Based Inference of Spatial-Stochastic Systems

Abstract Model parameter inference is a universal problem across science. This challenge is particularly pronounced in developmental biology, where faithful mechanistic descriptions require spatial-stochastic models with numerous parameters, yet quantitative empirical data often lack sufficient granularity due to experimental limitations. Parameterizing such complex models therefore necessitates methods that elaborate on classical Bayesian inference by incorporating notions of optimality and goal-orientation through low-dimensional objective functions that quantitatively encapsulate target system behavior. In this study, we contrast two such inference workflows and apply them to biophysically inspired spatial-stochastic models. Technically, both workflows employ simulation-based inference (SBI) methods: the first leverages a modern deep-learning technique known as sequential neural posterior estimation (SNPE), while the second relies on a classical optimization technique called simulated annealing (SA). We evaluate these workflows by inferring the parameters of two complementary models for the inner cell mass (ICM) lineage differentiation in the blastocyst-stage mouse embryo. This developmental biology system serves as a paradigmatic example of a highly robust and reproducible cell-fate proportioning process that self-organizes under strongly stochastic conditions, such as intrinsic biochemical noise and cell-cell signaling delays. Our results reveal that while both methods provide consistent model parameter estimates, the modern SBI workflow yields significantly richer inferred distributions at an equivalent computational cost. We identify the computational scenarios that favor the modern SBI method over its classical counterpart, and propose a plausible strategy to exploit the complementary strengths of both workflows for enhanced parameter space exploration.

A Two-Parameter Ridge Estimator for Handling Extreme Multicollinearity Problems in Logistic Regression

This paper introduces a robust two-parameter ridge estimator that is customized for logistic regression models, which tend to be sensitive to extreme multicollinearity problems. Inflated standard errors and unreliability in the results stem from the problem of multicollinearity characterized by high correlations among predictor variables in logistic regression model. Traditional approaches like the Maximum Likelihood Estimator (MLE) and one-parameter ridge-type estimators often perform poorly under these settings, thus calling for the development of more robust approaches. This new proposal is called New Biased Two Parameter (NBTP), which extends the ridge regression framework by introducing additional biasing parameters customized for an extreme multicollinearity problem. The paper combines a theoretical analysis with extensive Monte Carlo simulations and real application to Pena data. It demonstrates that the new estimator, New Biased Two Parameter (NBTP), provides much more stable and accurate parameter estimates than previous methods. The results underscore the importance of using robust estimation methods within logistic regression, especially when multicollinearity may be widespread in fields such as medical research, finance, and the social sciences.

A retinex inspired deep image prior model for despeckling and deblurring of aerial and satellite images using proximal gradient method

ABSTRACT Unsupervised learning models, particularly in the remote sensing domain, have gained significant attention in recent years. Various degradations in the satellite images, primarily occurring during acquisition, pose a substantial hurdle in obtaining reliable ground truth and extensive training data. The Deep Image Prior model (DIP) addresses these issues by performing restoration tasks using a single image, relying on the implicit regularization inherent in the network architecture. In this paper, we propose a novel approach, integrating the DIP model within the retinex framework to restore aerial and satellite images from the Gamma distributed speckles and linear shift-invariant Gaussian blur along with contrast enhancement using the alternating proximal gradient descent ascent (PGDA) method. Our proposed methodology combines implicit regularization with explicit total variational (TV) regularization, incorporating automated estimation of local regularization parameters. The data-fidelity component in the optimization function is formulated using the Bayesian Maximum A posteriori (MAP) estimate, assuming the speckles follow the Gamma distribution. Demonstration of despeckling and deblurring alone and in addition as a combined task is carried out on aerial and Synthetic Aperture Radar (SAR) images with different resolutions and polarization from various sources. Results obtained are compared with various state-of-the-art despeckling and deblurring models using distinct image quality metrics such as Equivalent Number of Looks (ENL), Contrast to Noise Ratio (CNR), Edge Preserving Index (EPI), Entropy, Global Contrast Factor (GCF), Natural Image Quality Evaluator (NIQE), Blind/Referenceless Image Spatial Quality Evaluator (BRISQUE) and Bradley-Terry (B-T) score based on the various factors. The quality of restored images depicted superior performance of the proposed method over the existing models under study.

Analysis of Variance of Tensor Product Reproducing Kernel Hilbert Spaces on Metric Spaces

Many methods have been developed to analyze complex data, such as non-Euclidean shape, network, and manifold data. However, there is a lack of methods for studying interactions among complex data. In this paper, we first propose a novel kernel function for a metric space and construct its associated reproducing kernel Hilbert space. The new nonstationary kernel function provides a flexible and powerful tool for learning complex structures in non-Euclidean data. We then construct an analysis of variance (ANOVA) decomposition of the nonparametric regression function defined on metric space, which provides a hierarchical structure for investigating the main effects and interactions. We develop estimation and computational methods for a semi-parametric model with a multivariate function on a product of metric spaces modeled by the ANOVA decomposition. We establish the convergence rates of parameter and nonparametric function estimates. The application of the proposed methods to the Alzheimer’s Disease Neuroimaging Initiative hippocampus shape data confirms some existing and suggests some new interactions among hippocampal regions. Simulations indicate that the proposed methods work well.

ON ESTIMATIONS IN AN EQUATION WITH A PARAMETER AND A DISCONTINUOUS OPERATOR

In a real reflexive Banach space, an equation with a parameter and a discontinuous nonlinear operator is considered. Both parameter estimations and operator norms are found for the equation. These estimations validate and define concretely the similar estimations obtained earlier in problems with a parameter for elliptic and ordinary differential equations with discontinuous right-hand sides.

Fringing effects in the operation of harmonic backing potential Kelvin probes

In this paper we present the effects of fringing on the measurement of the tip-sample capacitance for Kelvin probes driven by a harmonic backing potential. Moreover, we show that in this case it is still possible to obtain good estimations of operational parameters that allow for the fully controlled operation of harmonically driven Kelvin probes.

Estimating stress-strength reliability based on two-parameter exponential records in the presence of inter-record times

ABSTRACT This study addresses the problem of point and interval estimation for the reliability parameter in a stress-strength model when the data available consist of record values along with inter-record times, under two-parameter exponential distributions. The motivation for this paper arises from the need to improve reliability assessments in engineering and manufacturing contexts where products are subjected to stress conditions. Understanding the relationship between stress (the actual load on a system) and strength (the maximum load a system can withstand) is crucial for ensuring safety and performance. Record data, which encompass extreme observations, provide a valuable means to estimate the reliability parameter. We also explore the point and interval estimation of the reliability parameter when the scale parameters of the two exponential distributions are assumed to be equal. Monte Carlo simulations are conducted to assess the performance of the proposed estimates. Finally, we apply the results obtained in this paper to analyze two real data sets.