Superior exercise performance in lifelong Tibetan residents of 4,400 m compared with Tibetan residents of 3,658 m

Few environments challenge human populations more than high altitude, since the accompanying low oxygen pressures (hypoxia) are pervasive and impervious to cultural modification. Work capacity is an important factor in a population's ability to thrive in such an environment. The performance of work or exercise is a measure of the integrated functioning of the O₂ transport system, with maximal O₂ uptake (VO) a convenient index of that function. Hypoxia limits the ability to transport oxygen: maximal O₂ uptake decreases with ascent to high altitude, and years of high altitude residence do not restore sea level VO values. Since Tibetans live and work at some of the highest altitudes in the world, their ability to exercise at very high altitude (<4,000 m) may define the limits of human adaptation to hypoxia. We transported 20 Tibetan lifelong residents of ≥4,400 m down to 3,658 m in order to compare them with 16 previously studied Tibetan residents of Lhasa (3,658 m). The two groups of Tibetans were matched for age, weight, and height. All studies were performed in Lhasa within 3 days of the 4,400 m Tibetans' arrival. Standard test protocol and criteria were used for attaining VO on a Monark bicycle ergometer, while measuring oxygen uptake (VO₂, ml/kg − min STPD), heart rate (bpm), minute ventilation (VE, 1/min BTPS), and arterial oxygen saturation (Sa, %). The 4,400 m compared with 3,658 m residents had, at maximal effort, similar VO₂ (48.5 ± 1.2 vs. 51.2 ± 1.4 ml/kg − min, P = NS), higher workload attained (211 ± 6 vs. 177 ± 7 watts, P < 0.01), lower heart rate (176 ± 2 vs. 191 ± 2 bpm, P < 0.01), lower ventilation (127 ± 5 vs. 149 ± 5 l/min BTPS, P < 0.01), and similar Sa(81.9 ± 1.0 vs. 83.7 ± 1.2%, P = NS). Furthermore, over the range of submaximal workloads, 4,400 m compared with 3,658 m Tibetans had lower VO₂ (P < 0.01), lower heart rates (P < 0.01), and lower ventilation (P < 0.01) and Sa (P < 0.05). We conclude that Tibetans living at 4,400 m compared with those residing at 3,658 m achieve greater work performance for a given VO₂ at submaximal and maximal workloads with less cardiorespiratory effort. Am J Phys Anthropol 105:21–31, 1998. © 1998 Wiley-Liss, Inc.     

Estimation of Trichoderma QM 9414 biomass and growth rate by indirect means

Trichoderma QM 9414 was aerobically grown on glucose as the sole carbon and energy sources in a chemostat culture. The specific rates of glucose consumption (Q_G), oxygen consumption (Q), and carbon dioxide production (Q) at the steady state were measured to estimate the growth and maintenance requirements. From the results it was estimated that 2 mol adenosine triphosphate (ATP) were produced when1 mol NADH was oxidized through the respiratory chain of this microorganism. The true growth yield for ATP (Y_ATP) and specific ATP consumption rate for maintenance (Q) calculated with this value were 0.0106 g dry cell/mmol ATP and 5.2 mmol ATP/g dry cell/hr, respectively. Using the relationships between specific growth rate (μ) and (Q) and between μ and Q_G obtained from chemostat-culture data, cell and glucose concentration histories were estimated from the carbon dioxide production rate during the batch culture. The estimated cell concentrations agreed with the experimentally measured values. Glucose concentration were slightly overestimated.     

Levels of DNA strand breaks and superoxide in phorbol ester-treated human granulocytes

Phorbol ester treatment of granulocytes triggers release of superoxide (O) and a concomitant burst of DNA strand breaks. The relationship between the amount of O and the number of DNA breaks has not previously been explored. To quantify the relatively large amount of O generated over a 40-min period by 1 × 10⁶ granulocytes/mL, a discontinuous “10-min pulse” method employing cytochrome c was used; 140 nmol O per 1 × 10⁶ cells was detected. DNA strand breaks were quantified by fluorimetric analysis of DNA unwinding (FADU). To vary the level of O released by cells, inhibitors of the respiratory burst were used. Sodium fluoride (1–10 mM) and staurosporine (2–10 nM) both inhibited O production. In both cases, however, inhibition of strand breakage was considerably more pronounced than inhibition of O. Zinc chloride (50–200 μM) inhibited both O and DNA breaks, approximately equally. Dinophysistoxin-1 (okadaic acid) inhibited O production more effectively than it inhibited DNA breaks. O dismutes to H₂O₂, a reactive oxygen species known to cause DNA breaks. The addition of catalase to remove extracellular H₂O₂ had no effect on DNA breakage. Using pulse field gel electrophoresis, few double-stranded breaks were detected compared to the number detected by FADU, indicating that about 95% of breaks were single-stranded. The level of DNA breaks is not directly related to the amount of extracellular O or H₂O₂ in PMA-stimulated granulocytes. We conclude that either an intracellular pool of these reactive oxygen species is involved in breakage or that the metabolic inhibitors are affecting a novel strand break pathway. J. Cell. Biochem. 66:219–228, 1997. © 1997 Wiley-Liss Inc.     

Crystallization and preliminary X-ray analysis of Escherichia coli methionyl–tRNA formyltransferase

Methionyl–tRNA formyltransferase from Escherichia coli, a monomer of 34kDa, was overexpressed from its cloned gene fmt (Guillon, J.M., Mechulam, Y., Schmitter, J.M., Blanquet, S., and Fayat, G., J. Bacteriol. 174:4294–4301, 1992) and crystallized using ammonium sulphate as precipitant. The crystals are trigonal and have unit cell parameters a = b = 151.0Å, c = 81.8Å. They belong to space group P3₂21 and diffract to 2.0Å resolution. The structure is being solved by multiple isomorphous replacement. © 1996 Wiley-Liss, Inc.     

An Asymptotically Optimal Adaptive Selection Procedure in the Proportional Hazards Model with Conditionally Independent Censoring

Assume k independent populations are given which are distributed according to R, …,R (ϑ_i ∈ Θ ⊆ R ). Taking samples of size n the population with the smallest ϑ-value is to be selected. Using the framework of Le Cam's decision theory (Le Cam , 1986; Strasser , 1985) under mild regularity assumptions, an asymptotically optimal selection procedure is derived for the sequence of localized models. In the proportional hazards model with conditionally independent censoring, an asymptotically optimal adaptive selection procedure is constructed by substituting the unknown nuisance parameter by a kernel estimator.     

Co-oligopeptides containing two aromatic residues spaced by glycyl residues. X. Proton magnetic resonance study of co-oligopeptides of tryptophan and glycine

The ¹H-nmr spectra of co-oligopeptides of tryptophan and glycine with structure H-Gly-Trp-(Gly)_n-Trp-Gly-OH (n = 0–2) and those of several di- and tripeptides have been recorded at 360 MHz with CD₃OD solutions containing 0.1N NaOD. The assignment of resonance signals was generally possible by comparing the spectra of structurally related peptides with each other. In order to solve the remaining ambiguities in the assignment, H-(αL,βS)(α,β-d₂)Trp-OH, H-Trp-(αL,βS)(α,β-d₂)Trp-OH, and H-Trp-(δ¹,ε²,ζ²,ζ³,η²-d₅)Trp-OH have been prepared and their spectra compared with those of the undeuterated compounds. The distribution of rotamers around the χ₁ and (in two cases) χ₂ torsion angles of the side chains has been obtained from the vicinal coupling constants ³J and from the long-range coupling constants ⁴J. These data and an analysis of the chemical shifts of the Gly-C^α protons suggest that the orientation of the aromatic side chain is influenced by the following order of decreasing interaction with the functional groups at N- and C-side: -NH₂ > –NHCO– > –CONH–> –COO^?. This rule does not hold for the second Trp residue of di- and tripeptides containing the -Trp-Trp- sequence, which has tentatively been attributed to steric effects.     

Polynucleotides. XI. Thermodynamics of (A) N -2(U) infinity from the dependence of T m N on oligomer length

The variation in the helix-coil transition temperature, T_m^N, with oligomer length, N, for the system ((I)) has been examined. The results for N = 4-13, measured in 0.2M Na+, have been analyzed in terms of the expression of Blake (1972): ((II)) where c_m is the free oligomer concentration at T_m^N, and V_r^f is the thermodynamic free volume available to a helical base-triplet residue. The correlation coefficient for the fit to expression (II) of data obtained over a 50° temperature range is 0.997 when ΔH_r = ?12.6 kcal/mole of base-triplets (independent of oligomer length (N ? 4) or temperature), the value previously obtained from both calorimetry of (A)_∞·2(U)_∞ and (A)₄ concentration dependence of T_m. It is found that V_r^f = 8.0 × 10^?4 1/mole (± 30%) or 1.33 ų per helical base-triplet, and is constant with temperature. A maximum value for V_r^f of 21.0 × 10^?4 1/M (± 1.3%), equivalent to 3.54 ų per helical basetriplet is obtained by the same treatment of the helix-coil transition data for the three-stranded helix formed by adenosine (N = 1) and 2(U)_∞ obtained by Davies and Davidson (1971).     

Observation of a sterically unfavorable side-chain conformation in a leucyl residue: Crystal and molecular structure of L-leucyl–L-leucine · DMSO solvate

The crystal structure of a dipeptide L -leucyl–L -leucine (C₁₂H₂₄N₂O₃) has been determined. The crystals are monoclinic, space group P2₁, with a = 5.434(4) Å, b = 15.712(7) Å, c = 11.275(2) Å, β = 100.41(1)°, and Z = 2. The crystals contain one molecule of dimethyl sulfoxide (DMSO) as solvent of crystallization for each dipeptide molecule. The structure has been solved by direct methods and refined to a final R index of 0.059 for 920 reflections (sinθ/λ ? 0.60 Å^?1) with I ? 2σ (I). The trans peptide unit shows substantial degree of non-planarity (Δω = 14°). The peptide backbone adopts an extended conformation with torsion angles of ψ₁ = 138(1)°, ω₁ = 166(1)°, ?₂ = ? 149.3(7)°, ψ₂₁ = 164.2(7)°, and ψ₂₂ = ? 15(1)°. For the first leucyl residue, the side-chain conformation is specified by the torsion angles ¹χ₁ = 176.7(7)°, ¹χ₂₁ = 62(1)°, ¹χ₂₂ = ? 177.4(8)°; the second leucyl residue adopts a Sterically unfavorable conformation with ²χ₁ = 61(1)°, ²χ₂₁ = 97(1)°, and ²χ₂₂ = ?151(1)°. The packing involves head-to-tail interaction of peptide molecules and segregation of polar and nonpolar regions. The DMSO molecule is strongly hydrogen bonded to the terminal NH group. © 1994 John Wiley & Sons, Inc.     

Intracerebral quantitative chromophore estimation from reflectance spectra captured during deep brain stimulation implantation

Quantification of blood fraction (f_blood), blood oxygenation (S), melanin, lipofuscin and oxidised and reduced Cytochrome aa 3 and c was done from diffuse reflectance spectra captured in cortex, white matter, globus pallidus internus (GPi) and subthalamus during stereotactic implantations of 29 deep brain stimulation (DBS) electrodes with the aim of investigating whether the chromophores can give physiological information about the targets for DBS. Double‐sided Mann‐Whitney U ‐tests showed more lipofuscin in GPi compared to white matter and subthalamus (p < 0.05). Compared to the other structures, f_bloodwas significantly higher in cortex (p < 0.05) and S lower in GPi (p < 0.05). Median values and range for f_blood were 1.0 [0.2–6.0]% in the cortex, 0.3 [0.1–8.2]% in white matter, 0.2 [0.1–0.8]% in the GPi and 0.2 [0.1–11.7]% in the subthalamus. Corresponding values for S was 20 [0–81]% in the cortex, 29 [0–78]% in white matter, 0 [0–0]% in the GPi and 0 [0–92]% in the subthalamus. In conclusion, the measurements indicate very low oxygenation and blood volume for DBS patients, especially in the GPi. It would be of great interest to investigate whether this is due to the disease, the normal situation or an artefact of doing invasive measurements. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Letter: The magnitude of intramolecular DNA optical absorbance with variation in (Na+) and GC base composition: for special application to DNA reassociation studies.

The magnitude of intramolecular DNA optical absorbance is presented as a function of [Na⁺] and GC composition of the DNA. The data are presented as a ratio of absorbances A₀/A₀ for the DNA at the denaturing temperature (T_d) and renaturing temperature (T_r) under the given conditions. All ratios were determined for T_r corresponding to the temperature optimum (T_m ? T_r = 25°C) in DNA reassociation rate. This fact, coupled with the convenient A₀/A₀ ratio representation, permits the quick estimation of the magnitude of this optical effect in DNA reassociation reactions over a wide range of experimental conditions.     

Characterization of group C meningococcal polysaccharide by light-scattering spectroscopy. III. Determination of molecular weight, radius of gyration, and translational diffusional coefficient.

Group-specific polysaccharides isolated by means of a cetavlon procedure are immunogenic in man and induce protective immunity against meningococcal meningitis. Minute quantities of the polymers in solution can act as vaccines. We now report the first characterization of a fractionated (C-1) group C polysaccharide in 0.4KM KCl and 0.05M sodium acetate by means of light-scattering spectroscopy. Independent measurements of refractive index increments, absolute scattered intensities, angular scattering intensities and line widths as a function of scattering angles and delay times at different concentrations using incident wavelengths of 632.8 nm from a He–Ne laser and of 488 nm from an argon–ion laser yield information on aggregation properties, molecular weight (M_r), radius of gyration 〈r⁰_g〉^1/2_z, translational diffusion coefficient 〈D〉⁰_z, and second virial coefficients A₂ and B₂ of C-1 polysaccharide. At relatively high ionic strength (0.04M KCl + 0.05M sodium acetate), we obtain for the C-1 polysaccharide in solution M_r = 5.15 × 10⁵, 〈r²_g〉^1/2_z = 345 Å, A₂ = 1.25 × 10^?4 ml/g, 〈D〉 = 1.16 × 10^?7 cm²/sec with a corresponding Stokes radius of 240 Å and B₂ = 4.4 ml/g. A₂ and B₂ are the second virial coefficients from intensity- and diffusion-coefficient measurements. The C-1 polysaccharide aggregates in solution and behaves hydrodynamically like random coils. Viscosity and sedimentation studies further confirm our conclusions that the fractioned C-1 polysaccharide aggregates in solution and EDTA can partially break up those aggregates. However, the system remains polydisperse even after adding an excess amount of EDTA. The weight-average molecular weight of the C-1 polysaccharide in solution depends upon ionic strength and exhibits a minimum at ～0.2M KCl. Finally, viscosity, light-scattering, and sedimentation results all show that the aggregated macromolecular system behaves like random-coiled polymers with no measurable shape factors.     

Dynamic light scattering of aqueous solutions of linear aggregates induced by thermal denaturation of ovalbumin

Dynamic light scattering measurements were performed on dilute aqueous solutions of native ovalbumin (OA) and on those of linear OA aggregates induced by thermal denaturation at low ionic strength and neutral pH. The weight-average molecular weight M_w of four aggregates tested ranged from 1,700,000 to 5,500,000. The translational diffusion coefficient D₀ of native OA at infinite dilution was estimated as 8.70 × 10 ^?7 cm²/s, which gave 56.0 Å as the diameter of the rigid spherical particle. The intensity autocorrelation function of linear OA polymers was analyzed with the cumulant method to obtain the first cumulant Λ_e. The dependence of Λ_e on the scattering vector q at very low polymer concentration was found intermediate between those of a flexible chain and a rigid rod. The translational diffusion coefficient D_tr [≡ (T_e/q²)_{q → 0}] was in proportion to M, and the magnitude was in good agreement with a value calculated from the wormlike cylinder model with values of three parameters determined in an earlier study, M_L = 1600 Å^?1, d = 120 Å, and Q = 230 Å, where M_L, d, and Q are the molecular weight per unit length, diameter, and persistence length, respectively. Based on these results, a new model, to be called as the dimer model, was proposed to interpret the formation mechanism of linear OA polymers induced by thermal denaturation. © 1993 John Wiley & Sons, Inc.     

Inorganic carbon sources and biomass regulation in intensive microalgal cultures

Three freshwater and one marine algal species were grown under inorganic carbon limitation in laboratory continuous cultures. Comparisons were made between HCO₃^? alkalinity and bubbled CO₂ as carbon sources. HCO₃^? alkalinity was an excellent source of inorganic carbon below specific pH levels, but chemical precipitation at high pH placed an upper limit on productivity that was far lower than potential light-limiting levels. With bubbled CO₂ it was possible to achieve light limitation. The main factor controlling productivity was the mass flux of inorganic carbon added to the culture, which is the product of gas flow rate and influent P level. Small bubbles were more efficient than large bubbles at low gas flow rates and P levels, but led to froth flotation of algal cells and concomitant reductions in productivity at high bubble rates. At 1% CO₂ productivity was still dependent on mass fluxes of added carbon, but was independent of bubble size. At high bubble rates with 1% CO₂ narcosis was evident. Maximum yields occurred at intermediate dilution rates when inorganic carbon was supplied via bubbled gas.     

A kinetic analysis of hepatic microsomal activation of parathion and chlorpyrifos in control and phenobarbital-treated rats

A kinetic analysis of cytochrome P450-mediated desulfuration (activation) or dearylation (detoxication) showed that rat hepatic microsomes have a greater capacity to detoxify and a lower capacity to activate chlorpyrifos compared to parathion. Kinetic curves for the desulfuration of both parathion and chlorpyrifos were biphasic; K s of 0.23 and 71.3 μM were calculated for parathion, and 1.64 and 50.4 μM for chlorpyrifos. While phenobarbital (PB) exposure seemed to generally lower the K_mapp s for desulfuration except for the low K_m activity on chlorpyrifos, the results were not statistically significant. While the low K_m activity contributed 44 and 60% of the control V_max for parathion and chlorpyrifos, respectively, it contributed 50 and 17% in PB-treated rats. These studies have indicated the presence of a low K_m activity capable of functioning at very low substrate concentrations. A single dearylation K was calculated, 56.0 and 9.8 μM for parathion and chlorpyrifos, respectively. Phenobarbital exposure seemed to raise the Ks of dearylation; however, again, the results were not statistically significant. While numerous biochemical factors contribute to the overall toxicity levels of phosphorothionate insecticides, the in vitro efficiencies of hepatic microsomal desulfuration and dearylation of parathion and chlorpyrifos correspond to the acute toxicity levels.     

Bioleaching of Heavy Metal Polluted Sediment: Influence of Temperature and Oxygen (Part 1)

A remediation process for heavy metal polluted sediment has previously been developed in which the heavy metals are removed from the sediment by solid‐bed bioleaching using elemental sulfur (S⁰): the added S⁰ is oxidized by the indigenous microbes to sulfuric acid that dissolves the heavy metals which are finally extracted by percolating water. In this process, the temperature is a factor crucially affecting the rate of S⁰ oxidation and metal solubilization. Here, the effect of temperature on the kinetics of S⁰ oxidation has been studied: oxidized Weiße Elster River sediment (dredged near Leipzig, Germany) was mixed with 2 % S⁰, suspended in water and then leached at various temperatures. The higher the temperature was, the faster the S⁰ oxidized, and the more rapid the pH decreased. But temperatures above 35 °C slowed down S⁰ oxidation, and temperatures above 45 °C let the process – after a short period of acidification to pH 4.5 – stagnate. The latter may be explained by the presence of both neutrophilic to less acidophilic thermotolerant bacteria and acidophilic thermosensitive bacteria. Within 42 days, nearly complete S⁰ oxidation and maximum heavy metal solubilization only occurred at 30 to 45 °C. The measured pH(t) courses were used to model the rate of S⁰ oxidation depending on the temperature using an extended Arrhenius equation. Since molecular oxygen is another factor highly influencing the activity of S⁰‐oxidizing bacteria, the effect of dissolved O₂ (controlled by the O₂ content in the gas supplied) on S⁰ oxidation was studied in suspension: the indigenous S⁰‐oxidizing bacteria reacted quite tolerant to low O₂ concentrations; the rate of S⁰ oxidation – measured as the specific O₂ consumption – was not affected until the O₂ content of the suspension was below 0.05 mg/L, i.e., the S⁰‐oxidizing bacteria showed a high affinity to O₂ with a half‐saturation constant of about 0.01 mg/L. Stoichiometric coefficients describing the relationship between the mass of S⁰, O₂ and CO₂ consumed are scarcely available. The growth of S⁰‐oxidizing, obligate aerobic, autotrophic bacteria was, therefore, stoichiometrically balanced (by using a yield coefficient of Y_X/S = 0.146 g cells/g S⁰, calculated with data from the literature): 24.14 S⁰ + 29.21 O₂ + 27.14 H₂O + 5 CO₂ + NO₃^–→ C₅H₇O₂N + 24.14 SO₄^2– + 47.28 H⁺, which resulted in Y = 1.21 g O₂/g S⁰ and Y = 0.28 g CO₂/g S⁰.     

Determination of NOE "silent" dipolar interactions between magnetically equivalent nuclei: application to poly(dA).poly(dT)

The ratio of the spin–spin relaxation rate, R₂, to the selective spin–lattice relaxation rate, R, can be used to detect and determine the magnitude of dipolar interactions between magnetically equivalent unclei in macromolecules. We use this method to show that there is strong interaction between adjacent AH2 protons in poly(dA) · poly(dT). The largest possible AH2–AH2 distance that will account for the observed magnitude of the interaction is ～3.5 Å, provided the AH2 protons are located close (within 0.6 Å) to the helix axis. Structures with shorter AH2–AH2 separations could account for the nmr data, but they are rejected because they would reduce the interbase separation to unacceptably small values. A comparison of rates measured at 360 and 500 MHz shows that the chemical-shift anisotropy makes a negligible contribution to the observed relaxation rates.     

Equi-replicated balanced block designs generated by a balanced matrix

In this paper it is shown that if N= \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sum \limits_{i = 1}^{S_h} $\end{document} c_ihN_ih, where c_ih are some non-negative integer numbers and N_ih are such incidence matrices that A_h = \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sum \limits_{i = 1}^{S_h} $\end{document} i N_ih is a balanced matrix defined by SHAH (1959), for h = 1, 2,…, p, then a block design with an incidence matrix Ñ = [N, N,…,N] is an equi-replicated balanced block design. Here the balance of a block design is defined in terms of the matrix M₀ introduced by CALI?SKI (1971).     

Construction of Equi-replicated Balanced Block Designs with Block Sizes Exceeding the Number of Treatments

In this note it is shown that the block design with incidence matrix Ñ = [NN… N], where N = c_1hN_h + c_oh (11′–N_h). c_oh and c_1h are any non-negative integers and N_h,h = 1, 2,…,p, are incidence matrices of balanced incomplete block designs with the same number of treatments t, is a balanced block design with the block sizes exceeding the number of treatments. In derivation the matrix M₀, introduced by CALIński (1971) is utilized.     

Fed batch culture of Saccharomyces cerevisiae: A perspective of computer control to enhance the productivity in baker's yeast cultivation

A means to avoid the glucose effect in the production of baker's yeast from glucose and/or molasses in a fed batch culture by controlling the feed rate of fresh medium with an ad hoc measurement of the respiratory quotient, RQ, is presented. The feed rate is changed stepwise here such that the value of RQ ranges from 1.0 to 1.2 throughout the cultivation. Thus far, the specific growth rate based on the total cell mass and the growth yield obtained throughout are 0.24 hr^?1 and 0.55 g cell/g glucose. Prior to the experimental run mentioned above, equations to predetermine the feed rate and concentration of glucose in the feed are derived from the mass balance of limiting substrates (glucose). Since values of either RQ or I (Q x, oxygen consumption rate with respect to the total cell mass in the fermenter) can be measured quite easily and reliably, computer control of the fermentation in light of this information is discussed.     

Construction of Prediction Intervals in Location-Scale Families

Let x₁ ≤x₂ ≤x₃ … ≤x_r be the r smallest observations out of n observations from a location-scale family with density $ \frac{1}{\sigma}f\left({\frac{{x - \mu}}{\sigma}} \right) $ where μ and σ are the location and the scale parameters respectively. The goal is to construct a prediction interval of the form $ \left({\hat \mu + k_1 \hat \sigma,\,\hat \mu + k_2 \hat \sigma} \right) $ for a location-scale invariant function, T(Y) = T(Y₁, …, Y_m), of m future observations from the same distribution. Given any invariant estimators $ \hat \mu $ and $ \hat \sigma $, we have developed a general procedure for how to compute the values of k₁ and k₂. The two attractive features of the procedure are that it does not require any distributional knowledge of the joint distribution of the estimators beyond their first two raw moments and $ \hat \mu $ and $ \hat \sigma $ can be any invariant estimators of μ and σ. Examples with real data have been given and extensive simulation study showing the performance of the procedure is also offered.